Content check — Prealgebra, Chapter 10: Polynomials

Every problem in the chapter beside the book’s answer, a chapter at a time as you scroll.

Chapter 10: Polynomials

531 problems · 0 figures

Be Prepared 10.1 §10.1 source ↗

Simplify:

8 x + 3 x .

If you missed this problem, review Example 2.22.

Example 2.22 in the book ↗

Answer

11 x

Be Prepared 10.2 §10.1 source ↗

Subtract:

(5 n + 8) -

(2 n - 1) .

If you missed this problem, review Example 7.29.

Example 7.29 in the book ↗

Answer

3 n + 9

Be Prepared 10.3 §10.1 source ↗

Evaluate:

4 y^{2}

when

y = 5

If you missed this problem, review Example 2.18.

Example 2.18 in the book ↗

Answer

100

Try It 10.1 §10.1 source ↗

Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial.

ⓐ $z$

ⓑ $2 x^{3} - 4 x^{2} - x - 8$

ⓓ $9 - 4 y^{2}$

ⓔ $3 x^{7}$

Answer

ⓐ monomial

ⓑ polynomial

ⓓ binomial

ⓔ monomial

Try It 10.2 §10.1 source ↗

Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial.

ⓐ $y^{3} - 8$

ⓑ $9 x^{3} - 5 x^{2} - x$

ⓓ $− y^{4}$

ⓔ $w$

Answer

ⓐ binomial

ⓑ trinomial

ⓓ monomial

Try It 10.3 §10.1 source ↗

Find the degree of the following polynomials:

ⓐ $−6 y$

ⓑ $4 x - 1$

ⓓ $2 y^{2} + 3 y + 9$

ⓔ $−18$

Answer

ⓐ 1

ⓑ 1

ⓒ 4

ⓓ 2

ⓔ 0

Try It 10.4 §10.1 source ↗

Find the degree of the following polynomials:

ⓐ $47$

ⓑ $2 x^{2} - 8 x + 2$

ⓓ $y^{5} - 5 y^{3} + y$

ⓔ $9 a^{3}$

Answer

ⓐ 0

ⓑ 2

ⓒ 4

ⓓ 5

ⓔ 3

Try It 10.5 §10.1 source ↗

Add:

12 x^{2} + 5 x^{2} .

Answer

17x²

Try It 10.6 §10.1 source ↗

Add:

−11 y^{2} + 8 y^{2} .

Answer

−3y²

Try It 10.7 §10.1 source ↗

Subtract:

9 n - (−5 n) .

Answer

14n

Try It 10.8 §10.1 source ↗

Subtract:

−7 a^{3} -

(−5 a^{3}) .

Answer

−2a³

Try It 10.9 §10.1 source ↗

Add:

3 x^{2} +

3 y^{2} -

5 x^{2} .

Answer

−2x² + 3y²

Try It 10.10 §10.1 source ↗

Add:

2 a^{2} + b^{2} - 4 a^{2} .

Answer

−2a² + b²

Try It 10.11 §10.1 source ↗

Find the sum:

(3 x^{2} - 2 x + 8) +

(x^{2} - 6 x + 2) .

Answer

4x² − 8x + 10

Try It 10.12 §10.1 source ↗

Find the sum:

(7 y^{2} + 4 y - 6) +

(4 y^{2} + 5 y + 1) .

Answer

11y² + 9y − 5

Try It 10.13 §10.1 source ↗

Find the difference:

(6 y^{2} + 3 y - 1) -

(3 y^{2} - 4) .

Answer

3y² + 3y + 3

Try It 10.14 §10.1 source ↗

Find the difference:

(8 u^{2} - 7 u - 2) -

(5 u^{2} - 6 u - 4) .

Answer

3u² − u + 2

Try It 10.15 §10.1 source ↗

Subtract:

(4 n^{2} - 7 n - 3)

from

(8 n^{2} + 5 n - 3) .

Answer

4n² + 12n

Try It 10.16 §10.1 source ↗

Subtract:

(a^{2} - 4 a - 9)

from

(6 a^{2} + 4 a - 1) .

Answer

5a² + 8a + 8

Try It 10.17 §10.1 source ↗

Evaluate: $2 x^{2} + 4 x - 3$ when

ⓐ $x = 2$

ⓑ $x = −3$

Answer

ⓐ 13

ⓑ 3

Try It 10.18 §10.1 source ↗

Evaluate: $7 y^{2} - y - 2$ when

ⓐ $y = −4$

ⓑ $y = 0$

Answer

ⓐ 114

ⓑ −2

Try It 10.19 §10.1 source ↗

The polynomial

−8 t^{2} + 24 t + 4

gives the height, in feet, of a ball

t

seconds after it is tossed into the air, from an initial height of

4

feet. Find the height after

t = 3

seconds.

Answer

4 feet

Try It 10.20 §10.1 source ↗

The polynomial

−8 t^{2} + 24 t + 4

gives the height, in feet, of a ball

x

seconds after it is tossed into the air, from an initial height of

4

feet. Find the height after

t = 2

seconds.

Answer

20 feet

10.1-1 §10.1 source ↗

Identify Polynomials, Monomials, Binomials and Trinomials

In the following exercises, determine if each of the polynomials is a monomial, binomial, trinomial, or other polynomial.

$5 x + 2$

Answer

binomial

10.1-3 §10.1 source ↗

Identify Polynomials, Monomials, Binomials and Trinomials

In the following exercises, determine if each of the polynomials is a monomial, binomial, trinomial, or other polynomial.

$a^{2} + 9 a + 18$

Answer

trinomial

10.1-5 §10.1 source ↗

Identify Polynomials, Monomials, Binomials and Trinomials

In the following exercises, determine if each of the polynomials is a monomial, binomial, trinomial, or other polynomial.

$y^{3} -$ $8 y^{2} +$ $2 y -$ $16$

Answer

polynomial

10.1-7 §10.1 source ↗

Identify Polynomials, Monomials, Binomials and Trinomials

In the following exercises, determine if each of the polynomials is a monomial, binomial, trinomial, or other polynomial.

$23 y^{2}$

Answer

monomial

10.1-9 §10.1 source ↗

Determine the Degree of Polynomials

In the following exercises, determine the degree of each polynomial.

$8 a^{5} - 2 a^{3} + 1$

Answer

10.1-11 §10.1 source ↗

Determine the Degree of Polynomials

In the following exercises, determine the degree of each polynomial.

$3 x - 12$

Answer

10.1-13 §10.1 source ↗

Determine the Degree of Polynomials

In the following exercises, determine the degree of each polynomial.

$−13$

Answer

10.1-15 §10.1 source ↗

Add and Subtract Monomials

In the following exercises, add or subtract the monomials.

${6x}^{2} + 9 x^{2}$

Answer

15x²

10.1-17 §10.1 source ↗

Add and Subtract Monomials

In the following exercises, add or subtract the monomials.

$−12 u + 4 u$

Answer

−8u

10.1-19 §10.1 source ↗

Add and Subtract Monomials

In the following exercises, add or subtract the monomials.

$5 a + 7 b$

Answer

5a + 7b

10.1-21 §10.1 source ↗

Add and Subtract Monomials

In the following exercises, add or subtract the monomials.

Add: $4 a, - 3 b, - 8 a$

Answer

−4a −3b

10.1-23 §10.1 source ↗

Add and Subtract Monomials

In the following exercises, add or subtract the monomials.

$18 x - 2 x$

Answer

16x

10.1-25 §10.1 source ↗

Add and Subtract Monomials

In the following exercises, add or subtract the monomials.

Subtract $5 x^{6} from -$ $12 x^{6}$

Answer

−17x⁶

10.1-27 §10.1 source ↗

Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

$(4 y^{2} + 10 y + 3) +$ $(8 y^{2} - 6 y + 5)$

Answer

12y² + 4y + 8

10.1-29 §10.1 source ↗

Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

$(x^{2} + 6 x + 8) +$ $(−4 x^{2} + 11 x - 9)$

Answer

−3x² + 17x − 1

10.1-31 §10.1 source ↗

Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

$(3 a^{2} + 7) +$ $(a^{2} - 7 a - 18)$

Answer

4a² − 7a − 11

10.1-33 §10.1 source ↗

Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

$(6 m^{2} - 9 m - 3) -$ $(2 m^{2} + m - 5)$

Answer

4m² − 10m + 2

10.1-35 §10.1 source ↗

Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

$(z^{2} + 8 z + 9) -$ $(z^{2} - 3 z + 1)$

Answer

11z + 8

10.1-37 §10.1 source ↗

Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

$(12 s^{2} - 15 s) -$ $(s - 9)$

Answer

12s² − 16s + 9

10.1-39 §10.1 source ↗

Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

Find the sum of $(2 p^{3} - 8)$ and $(p^{2} + 9 p + 18)$

Answer

2p³ + p² + 9p + 10

10.1-41 §10.1 source ↗

Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

Subtract $(7 x^{2} - 4 x + 2)$ from $(8 x^{2} - x + 6)$

Answer

x² + 3x + 4

10.1-43 §10.1 source ↗

Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

Find the difference of $(w^{2} + w - 42)$ and $(w^{2} - 10 w + 24)$

Answer

11w − 66

10.1-45 §10.1 source ↗

Evaluate a Polynomial for a Given Value

In the following exercises, evaluate each polynomial for the given value.

$Evaluate 8 y^{2} -$ $3 y +$ $2$

ⓐ $y = 5$

ⓑ $y = −2$

Answer

ⓐ 187

ⓑ 40

ⓒ 2

10.1-47 §10.1 source ↗

Evaluate a Polynomial for a Given Value

In the following exercises, evaluate each polynomial for the given value.

$Evaluate 4 -$ $36 x when:$

ⓐ $x = 3$

ⓑ $x = 0$

Answer

ⓐ −104

ⓑ 4

10.1-49 §10.1 source ↗

Evaluate a Polynomial for a Given Value

In the following exercises, evaluate each polynomial for the given value.

A window washer drops a squeegee from a platform $275$ feet high. The polynomial $−16 t^{2} + 275$ gives the height of the squeegee $t$ seconds after it was dropped. Find the height after $t = 4$ seconds.

Answer

19 feet

10.1-51 §10.1 source ↗

Evaluate a Polynomial for a Given Value

In the following exercises, evaluate each polynomial for the given value.

Fuel Efficiency The fuel efficiency (in miles per gallon) of a bus going at a speed of $x$ miles per hour is given by the polynomial $-$ $\frac{1}{160} x^{2} +$ $\frac{1}{2} x .$ Find the fuel efficiency when $x = 40 mph.$

Answer

10 mpg

10.1-53 §10.1 source ↗

Evaluate a Polynomial for a Given Value

In the following exercises, evaluate each polynomial for the given value.

Using your own words, explain the difference between a monomial, a binomial, and a trinomial.

Answer

Answers will vary.

Be Prepared 10.4 §10.2 source ↗

Simplify:

\frac{3}{4} \cdot \frac{3}{4} .

If you missed the problem, review Example 4.25.

Example 4.25 in the book ↗

Answer

\frac{9}{16}

Be Prepared 10.5 §10.2 source ↗

Simplify:

(−2) (−2) (−2) .

If you missed the problem, review Example 3.52.

Example 3.52 in the book ↗

Answer

- 8

Try It 10.21 §10.2 source ↗

Simplify:

ⓐ $4^{3}$

ⓑ $11^{1}$

Answer

ⓐ 64

ⓑ 11

Try It 10.22 §10.2 source ↗

Simplify:

ⓐ $3^{4}$

ⓑ $21^{1}$

Answer

ⓐ 81

ⓐ 21

Try It 10.23 §10.2 source ↗

Simplify:

ⓐ ${(\frac{5}{8})}^{2}$

ⓑ ${(0.67)}^{2}$

Answer

ⓐ $\frac{25}{64}$

ⓑ $0.4489$

Try It 10.24 §10.2 source ↗

Simplify:

ⓐ ${(\frac{2}{5})}^{3}$

ⓑ ${(0.127)}^{2}$

Answer

ⓐ $\frac{8}{125}$

ⓑ $0.016129$

Try It 10.25 §10.2 source ↗

Simplify:

ⓐ ${(−2)}^{4}$

ⓑ ${−2}^{4}$

Answer

ⓐ 16

ⓑ −16

Try It 10.26 §10.2 source ↗

Simplify:

ⓐ ${(−8)}^{2}$

ⓑ ${−8}^{2}$

Answer

ⓐ 64

ⓑ −64

Try It 10.27 §10.2 source ↗

Simplify:

x^{7} \cdot x^{8} .

Answer

x ¹⁵

Try It 10.28 §10.2 source ↗

Simplify:

x^{5} \cdot x^{11} .

Answer

x ¹⁶

Try It 10.29 §10.2 source ↗

Simplify:

p^{9} \cdot p .

Answer

p ¹⁰

Try It 10.30 §10.2 source ↗

Simplify:

m \cdot m^{7} .

Answer

m ⁸

Try It 10.31 §10.2 source ↗

Simplify:

6 \cdot 6^{9} .

Answer

6¹⁰

Try It 10.32 §10.2 source ↗

Simplify:

9^{6} \cdot 9^{9} .

Answer

9¹⁵

Try It 10.33 §10.2 source ↗

Simplify:

y^{24} \cdot y^{19} .

Answer

y ⁴³

Try It 10.34 §10.2 source ↗

Simplify:

z^{15} \cdot z^{24} .

Answer

z ³⁹

Try It 10.35 §10.2 source ↗

Simplify:

x^{7} \cdot x^{5} \cdot x^{9} .

Answer

x ²¹

Try It 10.36 §10.2 source ↗

Simplify:

y^{3} \cdot y^{8} \cdot y^{4} .

Answer

y ¹⁵

Try It 10.37 §10.2 source ↗

Simplify:

ⓐ ${(x^{7})}^{4}$

ⓑ ${(7^{4})}^{8}$

Answer

ⓐ x²⁸

ⓑ 7³²

Try It 10.38 §10.2 source ↗

Simplify:

ⓐ ${(x^{6})}^{9}$

ⓑ ${(8^{6})}^{7}$

Answer

ⓐ x⁵⁴

ⓑ 8⁴²

Try It 10.39 §10.2 source ↗

Simplify:

{(−14 x)}^{2} .

Answer

196x²

Try It 10.40 §10.2 source ↗

Simplify:

{(−12 a)}^{2} .

Answer

144a²

Try It 10.41 §10.2 source ↗

Simplify:

{(−4 x y)}^{4} .

Answer

256x⁴y⁴

Try It 10.42 §10.2 source ↗

Simplify:

{(6 x y)}^{3} .

Answer

216x³y³

Try It 10.43 §10.2 source ↗

Simplify:

{(x^{4})}^{3} {(x^{7})}^{4} .

Answer

x ⁴⁰

Try It 10.44 §10.2 source ↗

Simplify:

{(y^{9})}^{2} {(y^{8})}^{3} .

Answer

y ⁴²

Try It 10.45 §10.2 source ↗

Simplify:

{(- 8 x^{4} y^{7})}^{3} .

Answer

−512x¹²y²¹

Try It 10.46 §10.2 source ↗

Simplify:

{(- 3 a^{5} b^{6})}^{4} .

Answer

81a²⁰b²⁴

Try It 10.47 §10.2 source ↗

Simplify:

{(7 n)}^{2} (2 n^{12}) .

Answer

98n¹⁴

Try It 10.48 §10.2 source ↗

Simplify:

{(4 m)}^{2} (3 m^{3}) .

Answer

48m⁵

Try It 10.49 §10.2 source ↗

Simplify:

{(u^{3} v^{2})}^{5} {(4 u v^{4})}^{3} .

Answer

64u¹⁸v²²

Try It 10.50 §10.2 source ↗

Simplify:

{(5 x^{2} y^{3})}^{2} {(3 x y^{4})}^{3} .

Answer

675x⁷y¹⁸

Try It 10.51 §10.2 source ↗

Multiply:

(7 x^{7}) (- 8 x^{4}) .

Answer

−56x¹¹

Try It 10.52 §10.2 source ↗

Multiply:

(- 9 y^{4}) (- 6 y^{5}) .

Answer

54y⁹

Try It 10.53 §10.2 source ↗

Multiply:

(\frac{4}{5} m^{4} n^{3}) (15 m n^{3}) .

Answer

12m⁵n⁶

Try It 10.54 §10.2 source ↗

Multiply:

(\frac{2}{3} p^{5} q) (18 p^{6} q^{7}) .

Answer

12p¹¹q⁸

10.2-55 §10.2 source ↗

Simplify Expressions with Exponents

In the following exercises, simplify each expression with exponents.

$4^{5}$

Answer

1,024

10.2-57 §10.2 source ↗

Simplify Expressions with Exponents

In the following exercises, simplify each expression with exponents.

${(\frac{1}{2})}^{2}$

Answer

\frac{1}{4}

10.2-59 §10.2 source ↗

Simplify Expressions with Exponents

In the following exercises, simplify each expression with exponents.

${(0.2)}^{3}$

Answer

0.008

10.2-61 §10.2 source ↗

Simplify Expressions with Exponents

In the following exercises, simplify each expression with exponents.

${(−5)}^{4}$

Answer

625

10.2-63 §10.2 source ↗

Simplify Expressions with Exponents

In the following exercises, simplify each expression with exponents.

${−5}^{4}$

Answer

−625

10.2-65 §10.2 source ↗

Simplify Expressions with Exponents

In the following exercises, simplify each expression with exponents.

${−10}^{4}$

Answer

−10,000

10.2-67 §10.2 source ↗

Simplify Expressions with Exponents

In the following exercises, simplify each expression with exponents.

${(- \frac{2}{3})}^{3}$

Answer

- \frac{8}{27}

10.2-69 §10.2 source ↗

Simplify Expressions with Exponents

In the following exercises, simplify each expression with exponents.

$- {0.5}^{2}$

Answer

−0.25

10.2-71 §10.2 source ↗

Simplify Expressions Using the Product Property of Exponents

In the following exercises, simplify each expression using the Product Property of Exponents.

$x^{3} \cdot x^{6}$

Answer

x ⁹

10.2-73 §10.2 source ↗

Simplify Expressions Using the Product Property of Exponents

In the following exercises, simplify each expression using the Product Property of Exponents.

$a \cdot a^{4}$

Answer

a ⁵

10.2-75 §10.2 source ↗

Simplify Expressions Using the Product Property of Exponents

In the following exercises, simplify each expression using the Product Property of Exponents.

$3^{5} \cdot 3^{9}$

Answer

3¹⁴

10.2-77 §10.2 source ↗

Simplify Expressions Using the Product Property of Exponents

In the following exercises, simplify each expression using the Product Property of Exponents.

$z \cdot z^{2} \cdot z^{3}$

Answer

z ⁶

10.2-79 §10.2 source ↗

Simplify Expressions Using the Product Property of Exponents

In the following exercises, simplify each expression using the Product Property of Exponents.

$x^{a} \cdot x^{2}$

Answer

x ^a+2

10.2-81 §10.2 source ↗

Simplify Expressions Using the Product Property of Exponents

In the following exercises, simplify each expression using the Product Property of Exponents.

$y^{a} \cdot y^{b}$

Answer

y ^a+b

10.2-83 §10.2 source ↗

Simplify Expressions Using the Power Property of Exponents

In the following exercises, simplify each expression using the Power Property of Exponents.

${(u^{4})}^{2}$

Answer

u ⁸

10.2-85 §10.2 source ↗

Simplify Expressions Using the Power Property of Exponents

In the following exercises, simplify each expression using the Power Property of Exponents.

${(y^{5})}^{4}$

Answer

y ²⁰

10.2-87 §10.2 source ↗

Simplify Expressions Using the Power Property of Exponents

In the following exercises, simplify each expression using the Power Property of Exponents.

${(10^{2})}^{6}$

Answer

10¹²

10.2-89 §10.2 source ↗

Simplify Expressions Using the Power Property of Exponents

In the following exercises, simplify each expression using the Power Property of Exponents.

${(x^{15})}^{6}$

Answer

x ⁹⁰

10.2-91 §10.2 source ↗

Simplify Expressions Using the Power Property of Exponents

In the following exercises, simplify each expression using the Power Property of Exponents.

${(x^{2})}^{y}$

Answer

x ^2y

10.2-93 §10.2 source ↗

Simplify Expressions Using the Power Property of Exponents

In the following exercises, simplify each expression using the Power Property of Exponents.

${(5^{x})}^{y}$

Answer

5^xy

10.2-95 §10.2 source ↗

Simplify Expressions Using the Product to a Power Property

In the following exercises, simplify each expression using the Product to a Power Property.

${(5 a)}^{2}$

Answer

25a²

10.2-97 §10.2 source ↗

Simplify Expressions Using the Product to a Power Property

In the following exercises, simplify each expression using the Product to a Power Property.

${(- 6 m)}^{3}$

Answer

−216m³

10.2-99 §10.2 source ↗

Simplify Expressions Using the Product to a Power Property

In the following exercises, simplify each expression using the Product to a Power Property.

${(4 r s)}^{2}$

Answer

16r²s²

10.2-101 §10.2 source ↗

Simplify Expressions Using the Product to a Power Property

In the following exercises, simplify each expression using the Product to a Power Property.

${(4 x y z)}^{4}$

Answer

256x⁴y⁴z⁴

10.2-103 §10.2 source ↗

Simplify Expressions by Applying Several Properties

In the following exercises, simplify each expression.

${(x^{2})}^{4} \cdot {(x^{3})}^{2}$

Answer

x ¹⁴

10.2-105 §10.2 source ↗

Simplify Expressions by Applying Several Properties

In the following exercises, simplify each expression.

${(a^{2})}^{6} \cdot {(a^{3})}^{8}$

Answer

a ³⁶

10.2-107 §10.2 source ↗

Simplify Expressions by Applying Several Properties

In the following exercises, simplify each expression.

${(3 x)}^{2} (5 x)$

Answer

45x³

10.2-109 §10.2 source ↗

Simplify Expressions by Applying Several Properties

In the following exercises, simplify each expression.

${(5 a)}^{2} {(2 a)}^{3}$

Answer

200a⁵

10.2-111 §10.2 source ↗

Simplify Expressions by Applying Several Properties

In the following exercises, simplify each expression.

${(2 m^{6})}^{3}$

Answer

8m¹⁸

10.2-113 §10.2 source ↗

Simplify Expressions by Applying Several Properties

In the following exercises, simplify each expression.

${(10 x^{2} y)}^{3}$

Answer

1,000x⁶y³

10.2-115 §10.2 source ↗

Simplify Expressions by Applying Several Properties

In the following exercises, simplify each expression.

${(−2 a^{3} b^{2})}^{4}$

Answer

16a¹²b⁸

10.2-117 §10.2 source ↗

Simplify Expressions by Applying Several Properties

In the following exercises, simplify each expression.

${(\frac{2}{3} x^{2} y)}^{3}$

Answer

\frac{8}{27} x^{6} y^{3}

10.2-119 §10.2 source ↗

Simplify Expressions by Applying Several Properties

In the following exercises, simplify each expression.

${(8 a^{3})}^{2} {(2 a)}^{4}$

Answer

1,024a¹⁰

10.2-121 §10.2 source ↗

Simplify Expressions by Applying Several Properties

In the following exercises, simplify each expression.

${(10 p^{4})}^{3} {(5 p^{6})}^{2}$

Answer

25,000p²⁴

10.2-123 §10.2 source ↗

Simplify Expressions by Applying Several Properties

In the following exercises, simplify each expression.

${(\frac{1}{2} x^{2} y^{3})}^{4} {(4 x^{5} y^{3})}^{2}$

Answer

x ¹⁸ y ¹⁸

10.2-125 §10.2 source ↗

Simplify Expressions by Applying Several Properties

In the following exercises, simplify each expression.

${(3 m^{2} n)}^{2} {(2 m n^{5})}^{4}$

Answer

144m⁸n²²

10.2-127 §10.2 source ↗

Multiply Monomials

In the following exercises, multiply the following monomials.

$(12 x^{2}) (−5 x^{4})$

Answer

−60x⁶

10.2-129 §10.2 source ↗

Multiply Monomials

In the following exercises, multiply the following monomials.

$(−8 u^{6}) (−9 u)$

Answer

72u⁷

10.2-131 §10.2 source ↗

Multiply Monomials

In the following exercises, multiply the following monomials.

$(\frac{1}{5} r^{8}) (20 r^{3})$

Answer

4r¹¹

10.2-133 §10.2 source ↗

Multiply Monomials

In the following exercises, multiply the following monomials.

$(4 a^{3} b) (9 a^{2} b^{6})$

Answer

36a⁵b⁷

10.2-135 §10.2 source ↗

Multiply Monomials

In the following exercises, multiply the following monomials.

$(\frac{4}{7} x y^{2}) (14 x y^{3})$

Answer

8x²y⁵

10.2-137 §10.2 source ↗

Multiply Monomials

In the following exercises, multiply the following monomials.

$(\frac{2}{3} x^{2} y) (\frac{3}{4} x y^{2})$

Answer

\frac{1}{2} x^{3} y^{3}

10.2-139 §10.2 source ↗

Multiply Monomials

In the following exercises, multiply the following monomials.

Email Janet emails a joke to six of her friends and tells them to forward it to six of their friends, who forward it to six of their friends, and so on. The number of people who receive the email on the second round is $6^{2},$ on the third round is $6^{3},$ as shown in the table. How many people will receive the email on the eighth round? Simplify the expression to show the number of people who receive the email.

Round	Number of people
$1$	$6$
$2$	$6^{2}$
$3$	$6^{3}$
$\dots$	$\dots$
$8$	$?$

Answer

1,679,616

10.2-141 §10.2 source ↗

Multiply Monomials

In the following exercises, multiply the following monomials.

Use the Product Property for Exponents to explain why $x \cdot x = x^{2} .$

Answer

Answers will vary.

10.2-143 §10.2 source ↗

Multiply Monomials

In the following exercises, multiply the following monomials.

Jorge thinks ${(\frac{1}{2})}^{2}$ is $1 .$ What is wrong with his reasoning?

Answer

Answers will vary.

Be Prepared 10.6 §10.3 source ↗

Distribute:

2 (x + 3) .

If you missed the problem, review Example 7.17.

Example 7.17 in the book ↗

Answer

2 x + 6

Be Prepared 10.7 §10.3 source ↗

Distribute:

−11 (4 - 3 a) .

If you missed the problem, review Example 7.26.

Example 7.26 in the book ↗

Answer

- 44 + 33 a

Be Prepared 10.8 §10.3 source ↗

Combine like terms:

x^{2} +

9 x +

7 x +

63 .

If you missed the problem, review Example 2.21.

Example 2.21 in the book ↗

Answer

x^{2} + 16 x + 63

Try It 10.55 §10.3 source ↗

Multiply:

6 (x + 8) .

Answer

6x + 48

Try It 10.56 §10.3 source ↗

Multiply:

2 (y + 12) .

Answer

2y + 24

Try It 10.57 §10.3 source ↗

Multiply:

y (y - 9) .

Answer

y² − 9y

Try It 10.58 §10.3 source ↗

Multiply:

p (p - 13) .

Answer

p² − 13p

Try It 10.59 §10.3 source ↗

Multiply:

8 x (x + 3 y) .

Answer

8x² + 24xy

Try It 10.60 §10.3 source ↗

Multiply:

3 r (6 r + s) .

Answer

18r² + 3rs

Try It 10.61 §10.3 source ↗

Multiply:

−4 y (8 y^{2} + 5 y - 9) .

Answer

−32y³ − 20y² + 36y

Try It 10.62 §10.3 source ↗

Multiply:

−6 x (9 x^{2} + x - 1) .

Answer

−54x³ − 6x² + 6x

Try It 10.63 §10.3 source ↗

Multiply:

3 x^{2} (4 x^{2} - 3 x + 9) .

Answer

12x⁴ − 9x³ + 27x²

Try It 10.64 §10.3 source ↗

Multiply:

8 y^{2} (3 y^{2} - 2 y - 4) .

Answer

24y⁴ − 16y³ − 32y²

Try It 10.65 §10.3 source ↗

Multiply:

(x + 8) p .

Answer

xp + 8p

Try It 10.66 §10.3 source ↗

Multiply:

(a + 4) p .

Answer

ap + 4p

Try It 10.67 §10.3 source ↗

Multiply:

(x + 8) (x + 9) .

Answer

x² + 17x + 72

Try It 10.68 §10.3 source ↗

Multiply:

(a + 4) (a + 5) .

Answer

a² + 9a + 20

Try It 10.69 §10.3 source ↗

Multiply:

(5 x + 9) (4 x + 3) .

Answer

20x² + 51x + 27

Try It 10.70 §10.3 source ↗

Multiply:

(10 m + 9) (8 m + 7) .

Answer

80m² + 142m + 63

Try It 10.71 §10.3 source ↗

Multiply:

(7 y + 1) (8 y - 3) .

Answer

56y² − 13y − 3

Try It 10.72 §10.3 source ↗

Multiply:

(3 x + 2) (5 x - 8) .

Answer

15x² − 14x − 16

Try It 10.73 §10.3 source ↗

Multiply:

(x + 5) (x - y) .

Answer

x² − xy + 5x − 5y

Try It 10.74 §10.3 source ↗

Multiply:

(x + 2 y) (x - 1) .

Answer

x² − x + 2xy − 2y

Try It 10.75 §10.3 source ↗

Multiply using the FOIL method:

(x + 7) (x + 8) .

Answer

x² + 15x + 56

Try It 10.76 §10.3 source ↗

Multiply using the FOIL method:

(y + 14) (y + 2) .

Answer

y² + 16y + 28

Try It 10.77 §10.3 source ↗

Multiply:

(y - 3) (y + 8) .

Answer

y² + 5y − 24

Try It 10.78 §10.3 source ↗

Multiply:

(q - 4) (q + 5) .

Answer

q² + q − 20

Try It 10.79 §10.3 source ↗

Multiply:

(4 a + 9) (5 a - 2) .

Answer

20a² + 37a − 18

Try It 10.80 §10.3 source ↗

Multiply:

(7 x + 4) (7 x - 8) .

Answer

49x² − 28x − 32

Try It 10.81 §10.3 source ↗

Multiply:

(12 x - y) (x - 5) .

Answer

12x² − 60x − xy + 5y

Try It 10.82 §10.3 source ↗

Multiply:

(6 a - b) (2 a - 9) .

Answer

12a² − 54a − 2ab + 9b

Try It 10.83 §10.3 source ↗

Multiply using the vertical method:

(4 m - 9) (3 m - 7) .

Answer

12m² − 55m + 63

Try It 10.84 §10.3 source ↗

Multiply using the vertical method:

(6 n - 5) (7 n - 2) .

Answer

42n² − 47n + 10

Try It 10.85 §10.3 source ↗

Multiply using the Distributive Property:

(y - 1) (y^{2} - 7 y + 2) .

Answer

y³ − 8y² + 9y − 2

Try It 10.86 §10.3 source ↗

Multiply using the Distributive Property:

(x + 2) (3 x^{2} - 4 x + 5) .

Answer

3x³ + 2x² − 3x + 10

Try It 10.87 §10.3 source ↗

Multiply using the Vertical Method:

(y - 1) (y^{2} - 7 y + 2) .

Answer

y³ − 8y² + 9y − 2

Try It 10.88 §10.3 source ↗

Multiply using the Vertical Method:

(x + 2) (3 x^{2} - 4 x + 5) .

Answer

3x³ + 2x² − 3x + 10

10.3-145 §10.3 source ↗

Multiply a Polynomial by a Monomial

In the following exercises, multiply.

$4 (x + 10)$

Answer

4x + 40

10.3-147 §10.3 source ↗

Multiply a Polynomial by a Monomial

In the following exercises, multiply.

$15 (r - 24)$

Answer

15r − 360

10.3-149 §10.3 source ↗

Multiply a Polynomial by a Monomial

In the following exercises, multiply.

$−3 (m + 11)$

Answer

−3m − 33

10.3-151 §10.3 source ↗

Multiply a Polynomial by a Monomial

In the following exercises, multiply.

$−8 (z - 5)$

Answer

−8z + 40

10.3-153 §10.3 source ↗

Multiply a Polynomial by a Monomial

In the following exercises, multiply.

$u (u + 5)$

Answer

u² + 5u

10.3-155 §10.3 source ↗

Multiply a Polynomial by a Monomial

In the following exercises, multiply.

$n (n^{2} - 3 n)$

Answer

n³ − 3n²

10.3-157 §10.3 source ↗

Multiply a Polynomial by a Monomial

In the following exercises, multiply.

$12 x (x - 10)$

Answer

12x² − 120x

10.3-159 §10.3 source ↗

Multiply a Polynomial by a Monomial

In the following exercises, multiply.

$−9 a (3 a + 5)$

Answer

−27a² − 45a

10.3-161 §10.3 source ↗

Multiply a Polynomial by a Monomial

In the following exercises, multiply.

$6 x (4 x + y)$

Answer

24x² + 6xy

10.3-163 §10.3 source ↗

Multiply a Polynomial by a Monomial

In the following exercises, multiply.

$5 p (11 p - 5 q)$

Answer

55p² − 25pq

10.3-165 §10.3 source ↗

Multiply a Polynomial by a Monomial

In the following exercises, multiply.

$3 (v^{2} + 10 v + 25)$

Answer

3v² + 30v + 75

10.3-167 §10.3 source ↗

Multiply a Polynomial by a Monomial

In the following exercises, multiply.

$2 n (4 n^{2} - 4 n + 1)$

Answer

8n³ − 8n² + 2n

10.3-169 §10.3 source ↗

Multiply a Polynomial by a Monomial

In the following exercises, multiply.

$−8 y (y^{2} + 2 y - 15)$

Answer

−8y³ − 16y² + 120y

10.3-171 §10.3 source ↗

Multiply a Polynomial by a Monomial

In the following exercises, multiply.

$5 q^{3} (q^{2} - 2 q + 6)$

Answer

5q⁵ − 10q⁴ + 30q³

10.3-173 §10.3 source ↗

Multiply a Polynomial by a Monomial

In the following exercises, multiply.

$−4 z^{2} (3 z^{2} + 12 z - 1)$

Answer

−12z⁴ − 48z³ + 4z²

10.3-175 §10.3 source ↗

Multiply a Polynomial by a Monomial

In the following exercises, multiply.

$(2 y - 9) y$

Answer

2y² − 9y

10.3-177 §10.3 source ↗

Multiply a Polynomial by a Monomial

In the following exercises, multiply.

$(w - 6) \cdot 8$

Answer

8w − 48

10.3-179 §10.3 source ↗

Multiply a Binomial by a Binomial

In the following exercises, multiply the following binomials using: ⓐ the Distributive Property ⓑ the FOIL method ⓒ the Vertical method

$(x + 4) (x + 6)$

Answer

x² + 10x + 24

10.3-181 §10.3 source ↗

Multiply a Binomial by a Binomial

In the following exercises, multiply the following binomials using: ⓐ the Distributive Property ⓑ the FOIL method ⓒ the Vertical method

$(n + 12) (n - 3)$

Answer

n² + 9n − 36

10.3-183 §10.3 source ↗

In the following exercises, multiply the following binomials. Use any method.

$(y + 8) (y + 3)$

Answer

y² + 11y + 24

10.3-185 §10.3 source ↗

In the following exercises, multiply the following binomials. Use any method.

$(a + 6) (a + 16)$

Answer

a² + 22a + 96

10.3-187 §10.3 source ↗

In the following exercises, multiply the following binomials. Use any method.

$(u - 5) (u - 9)$

Answer

u² − 14u + 45

10.3-189 §10.3 source ↗

In the following exercises, multiply the following binomials. Use any method.

$(z - 10) (z - 22)$

Answer

z² − 32z + 220

10.3-191 §10.3 source ↗

In the following exercises, multiply the following binomials. Use any method.

$(x - 4) (x + 7)$

Answer

x² + 3x − 28

10.3-193 §10.3 source ↗

In the following exercises, multiply the following binomials. Use any method.

$(v + 12) (v - 5)$

Answer

v² + 7v − 60

10.3-195 §10.3 source ↗

In the following exercises, multiply the following binomials. Use any method.

$(6 n + 5) (n + 1)$

Answer

6n² + 11n + 5

10.3-197 §10.3 source ↗

In the following exercises, multiply the following binomials. Use any method.

$(2 m - 9) (10 m + 1)$

Answer

20m² − 88m − 9

10.3-199 §10.3 source ↗

In the following exercises, multiply the following binomials. Use any method.

$(4 c - 1) (4 c + 1)$

Answer

16c² − 1

10.3-201 §10.3 source ↗

In the following exercises, multiply the following binomials. Use any method.

$(3 u - 8) (5 u - 14)$

Answer

15u² − 82u + 112

10.3-203 §10.3 source ↗

In the following exercises, multiply the following binomials. Use any method.

$(a + b) (2 a + 3 b)$

Answer

2a² + 5ab + 3b²

10.3-205 §10.3 source ↗

In the following exercises, multiply the following binomials. Use any method.

$(5 x - y) (x - 4)$

Answer

5x² − 20x − xy + 4y

10.3-207 §10.3 source ↗

Multiply a Trinomial by a Binomial

In the following exercises, multiply using ⓐ the Distributive Property and ⓑ the Vertical Method.

$(u + 4) (u^{2} + 3 u + 2)$

Answer

u³ + 7u² + 14u + 8

10.3-209 §10.3 source ↗

Multiply a Trinomial by a Binomial

In the following exercises, multiply using ⓐ the Distributive Property and ⓑ the Vertical Method.

$(a + 10) (3 a^{2} + a - 5)$

Answer

3a³ + 31a² + 5a − 50

10.3-211 §10.3 source ↗

In the following exercises, multiply. Use either method.

$(y - 6) (y^{2} - 10 y + 9)$

Answer

y³ − 16y² + 69y − 54

10.3-213 §10.3 source ↗

In the following exercises, multiply. Use either method.

$(2 x + 1) (x^{2} - 5 x - 6)$

Answer

2x³ − 9x² − 17x − 6

10.3-215 §10.3 source ↗

In the following exercises, multiply. Use either method.

Mental math You can use binomial multiplication to multiply numbers without a calculator. Say you need to multiply $13$ times $15 .$ Think of $13$ as $10 + 3$ and $15$ as $10 + 5 .$

ⓐ Multiply $(10 + 3) (10 + 5)$ by the FOIL method.

ⓑ Multiply $13 \cdot 15$ without using a calculator.

Answer

ⓐ 195

ⓑ 195

10.3-217 §10.3 source ↗

In the following exercises, multiply. Use either method.

Which method do you prefer to use when multiplying two binomials—the Distributive Property, the FOIL method, or the Vertical Method? Why?

Answer

Answers will vary.

Be Prepared 10.9 §10.4 source ↗

Simplify:

\frac{8}{24} .

If you missed the problem, review Example 4.19.

Example 4.19 in the book ↗

Answer

\frac{1}{3}

Be Prepared 10.10 §10.4 source ↗

Simplify:

{(2 m^{3})}^{5} .

If you missed the problem, review Example 10.23.

Example 10.23 in the book ↗

Answer

32 m^{15}

Be Prepared 10.11 §10.4 source ↗

Simplify:

\frac{12 x^{}}{12 y} .

If you missed the problem, review Example 4.23.

Example 4.23 in the book ↗

Answer

\frac{x}{y}

Try It 10.89 §10.4 source ↗

Simplify:

ⓐ $\frac{x^{12}}{x^{9}}$

ⓑ $\frac{7^{14}}{7^{5}}$

Answer

ⓐ x³

ⓑ 7⁹

Try It 10.90 §10.4 source ↗

Simplify:

ⓐ $\frac{y^{23}}{y^{17}}$

ⓑ $\frac{8^{15}}{8^{7}}$

Answer

ⓐ y⁶

ⓑ 8⁸

Try It 10.91 §10.4 source ↗

Simplify:

ⓐ $\frac{x^{8}}{x^{15}}$

ⓑ $\frac{12^{11}}{12^{21}}$

Answer

ⓐ $\frac{1}{x^{7}}$

ⓑ $\frac{1}{12^{10}}$

Try It 10.92 §10.4 source ↗

Simplify:

ⓐ $\frac{m^{17}}{m^{26}}$

ⓑ $\frac{7^{8}}{7^{14}}$

Answer

ⓐ $\frac{1}{m^{9}}$

ⓑ $\frac{1}{7^{6}}$

Try It 10.93 §10.4 source ↗

Simplify:

ⓐ $\frac{b^{19}}{b^{11}}$

ⓑ $\frac{z^{5}}{z^{11}}$

Answer

ⓐ $b^{8}$

ⓑ $\frac{1}{z^{6}}$

Try It 10.94 §10.4 source ↗

Simplify:

ⓐ $\frac{p^{9}}{p^{17}}$

ⓑ $\frac{w^{13}}{w^{9}}$

Answer

ⓐ $\frac{1}{p^{8}}$

ⓑ $w^{4}$

Try It 10.95 §10.4 source ↗

Simplify:

ⓐ $17^{0}$

ⓑ $m^{0}$

Answer

ⓐ 1

ⓑ 1

Try It 10.96 §10.4 source ↗

Simplify:

ⓐ $k^{0}$

ⓑ $29^{0}$

Answer

ⓐ 1

ⓑ 1

Try It 10.97 §10.4 source ↗

Simplify:

{(−4 y)}^{0} .

Answer

Try It 10.98 §10.4 source ↗

Simplify:

{(\frac{2}{3} x)}^{0} .

Answer

Try It 10.99 §10.4 source ↗

Simplify:

ⓐ ${(7 x^{2} y)}^{0}$

ⓑ $7 x^{2} y^{0}$

Answer

ⓐ 1

ⓑ 7x²

Try It 10.100 §10.4 source ↗

Simplify:

ⓐ $−23 x^{2} y^{0}$

ⓑ ${(−23 x^{2} y)}^{0}$

Answer

ⓐ −23x²

ⓑ 1

Try It 10.101 §10.4 source ↗

Simplify:

ⓐ ${(\frac{7}{9})}^{2}$

ⓑ ${(\frac{y}{8})}^{3}$

Answer

ⓐ $\frac{49}{81}$

ⓑ $\frac{y^{3}}{512}$

Try It 10.102 §10.4 source ↗

Simplify:

ⓐ ${(\frac{1}{8})}^{2}$

ⓑ ${(\frac{−5}{m})}^{3}$

Answer

ⓐ $\frac{1}{64}$

ⓑ $- \frac{125}{m^{3}}$

Try It 10.103 §10.4 source ↗

Simplify:

\frac{{(a^{4})}^{5}}{a^{9}} .

Answer

a ¹¹

Try It 10.104 §10.4 source ↗

Simplify:

\frac{{(b^{5})}^{6}}{b^{11}} .

Answer

b ¹⁹

Try It 10.105 §10.4 source ↗

Simplify:

\frac{k^{11}}{{(k^{3})}^{3}} .

Answer

k ²

Try It 10.106 §10.4 source ↗

Simplify:

\frac{d^{23}}{{(d^{4})}^{6}} .

Answer

\frac{1}{d}

Try It 10.107 §10.4 source ↗

Simplify:

{(\frac{f^{14}}{f^{8}})}^{2} .

Answer

f ¹²

Try It 10.108 §10.4 source ↗

Simplify:

{(\frac{b^{6}}{b^{11}})}^{2} .

Answer

\frac{1}{b^{10}}

Try It 10.109 §10.4 source ↗

Simplify:

{(\frac{m^{3}}{n^{8}})}^{5} .

Answer

\frac{m^{15}}{n^{40}}

Try It 10.110 §10.4 source ↗

Simplify:

{(\frac{t^{10}}{u^{7}})}^{2} .

Answer

\frac{t^{20}}{u^{14}}

Try It 10.111 §10.4 source ↗

Simplify:

{(\frac{5 b}{9 c^{3}})}^{2} .

Answer

\frac{25 b^{2}}{81 c^{6}}

Try It 10.112 §10.4 source ↗

Simplify:

{(\frac{4 p^{4}}{7 q^{5}})}^{3} .

Answer

\frac{64 p^{12}}{343 q^{15}}

Try It 10.113 §10.4 source ↗

Simplify:

\frac{{(y^{4})}^{4} {(y^{3})}^{5}}{{(y^{7})}^{6}} .

Answer

\frac{1}{y^{11}}

Try It 10.114 §10.4 source ↗

Simplify:

\frac{{(3 x^{4})}^{2} {(x^{3})}^{4}}{{(x^{5})}^{3}} .

Answer

9x⁵

Try It 10.115 §10.4 source ↗

Find the quotient:

63 x^{8} \div 9 x^{4} .

Answer

7x⁴

Try It 10.116 §10.4 source ↗

Find the quotient:

96 y^{11} \div 6 y^{8} .

Answer

16y³

Try It 10.117 §10.4 source ↗

Find the quotient:

\frac{−84 x^{8} y^{3}}{7 x^{10} y^{2}} .

Answer

- \frac{12 y}{x^{2}}

Try It 10.118 §10.4 source ↗

Find the quotient:

\frac{−72 a^{4} b^{5}}{−8 a^{9} b^{5}} .

Answer

\frac{9}{a^{5}}

Try It 10.119 §10.4 source ↗

Find the quotient:

\frac{16 a^{7} b^{6}}{24 a b^{8}} .

Answer

\frac{2 a^{6}}{3 b^{2}}

Try It 10.120 §10.4 source ↗

Find the quotient:

\frac{27 p^{4} q^{7}}{−45 p^{12} q^{}} .

Answer

- \frac{3 q^{6}}{5 p^{8}}

Try It 10.121 §10.4 source ↗

Find the quotient:

\frac{28 x^{5} y^{14}}{49 x^{9} y^{12}} .

Answer

\frac{4 y^{2}}{7 x^{4}}

Try It 10.122 §10.4 source ↗

Find the quotient:

\frac{30 m^{5} n^{11}}{48 m^{10} n^{14}} .

Answer

\frac{5}{8 m^{5} n^{3}}

Try It 10.123 §10.4 source ↗

Find the quotient:

\frac{(3 x^{4} y^{5}) (8 x^{2} y^{5})}{12 x^{5} y^{8}} .

Answer

2xy²

Try It 10.124 §10.4 source ↗

Find the quotient:

\frac{(−6 a^{6} b^{9}) (−8 a^{5} b^{8})}{−12 a^{10} b^{12}} .

Answer

−4ab⁵

10.4-219 §10.4 source ↗

Simplify Expressions Using the Quotient Property of Exponents

In the following exercises, simplify.

$\frac{4^{8}}{4^{2}}$

Answer

4⁶

10.4-221 §10.4 source ↗

Simplify Expressions Using the Quotient Property of Exponents

In the following exercises, simplify.

$\frac{x^{12}}{x^{3}}$

Answer

x ⁹

10.4-223 §10.4 source ↗

Simplify Expressions Using the Quotient Property of Exponents

In the following exercises, simplify.

$\frac{r^{5}}{r}$

Answer

r ⁴

10.4-225 §10.4 source ↗

Simplify Expressions Using the Quotient Property of Exponents

In the following exercises, simplify.

$\frac{y^{4}}{y^{20}}$

Answer

\frac{1}{y^{16}}

10.4-227 §10.4 source ↗

Simplify Expressions Using the Quotient Property of Exponents

In the following exercises, simplify.

$\frac{10^{3}}{10^{15}}$

Answer

\frac{1}{10^{12}}

10.4-229 §10.4 source ↗

Simplify Expressions Using the Quotient Property of Exponents

In the following exercises, simplify.

$\frac{a}{a^{9}}$

Answer

\frac{1}{a^{8}}

10.4-231 §10.4 source ↗

Simplify Expressions with Zero Exponents

In the following exercises, simplify.

$5^{0}$

Answer

10.4-233 §10.4 source ↗

Simplify Expressions with Zero Exponents

In the following exercises, simplify.

$a^{0}$

Answer

10.4-235 §10.4 source ↗

Simplify Expressions with Zero Exponents

In the following exercises, simplify.

$- 7^{0}$

Answer

−1

10.4-237 §10.4 source ↗

Simplify Expressions with Zero Exponents

In the following exercises, simplify.

ⓐ ${(10 p)}^{0}$

ⓑ $10 p^{0}$

Answer

ⓐ 1

ⓑ 10

10.4-239 §10.4 source ↗

Simplify Expressions with Zero Exponents

In the following exercises, simplify.

ⓐ ${(−27 x^{5} y)}^{0}$

ⓑ $−27 x^{5} y^{0}$

Answer

ⓐ 1

ⓑ −27x⁵

10.4-241 §10.4 source ↗

Simplify Expressions with Zero Exponents

In the following exercises, simplify.

ⓐ $15^{0}$

ⓑ $15^{1}$

Answer

ⓐ 1

ⓑ 15

10.4-243 §10.4 source ↗

Simplify Expressions with Zero Exponents

In the following exercises, simplify.

$2 \cdot x^{0} + 5 \cdot y^{0}$

Answer

10.4-245 §10.4 source ↗

Simplify Expressions Using the Quotient to a Power Property

In the following exercises, simplify.

${(\frac{3}{2})}^{5}$

Answer

\frac{243}{32}

10.4-247 §10.4 source ↗

Simplify Expressions Using the Quotient to a Power Property

In the following exercises, simplify.

${(\frac{m}{6})}^{3}$

Answer

\frac{m^{3}}{216}

10.4-249 §10.4 source ↗

Simplify Expressions Using the Quotient to a Power Property

In the following exercises, simplify.

${(\frac{x}{y})}^{10}$

Answer

\frac{x^{10}}{y^{10}}

10.4-251 §10.4 source ↗

Simplify Expressions Using the Quotient to a Power Property

In the following exercises, simplify.

${(\frac{a}{3 b})}^{2}$

Answer

\frac{a^{2}}{9 b^{2}}

10.4-253 §10.4 source ↗

Simplify Expressions by Applying Several Properties

In the following exercises, simplify.

$\frac{{(x^{2})}^{4}}{x^{5}}$

Answer

x ³

10.4-255 §10.4 source ↗

Simplify Expressions by Applying Several Properties

In the following exercises, simplify.

$\frac{{(u^{3})}^{4}}{u^{10}}$

Answer

u ²

10.4-257 §10.4 source ↗

Simplify Expressions by Applying Several Properties

In the following exercises, simplify.

$\frac{y^{8}}{{(y^{5})}^{2}}$

Answer

\frac{1}{y^{2}}

10.4-259 §10.4 source ↗

Simplify Expressions by Applying Several Properties

In the following exercises, simplify.

$\frac{r^{5}}{r^{4} \cdot r}$

Answer

10.4-261 §10.4 source ↗

Simplify Expressions by Applying Several Properties

In the following exercises, simplify.

${(\frac{x^{2}}{x^{8}})}^{3}$

Answer

\frac{1}{x^{18}}

10.4-263 §10.4 source ↗

Simplify Expressions by Applying Several Properties

In the following exercises, simplify.

${(\frac{a^{4} \cdot a^{6}}{a^{3}})}^{2}$

Answer

a ¹⁴

10.4-265 §10.4 source ↗

Simplify Expressions by Applying Several Properties

In the following exercises, simplify.

$\frac{{(y^{3})}^{5}}{{(y^{4})}^{3}}$

Answer

y ³

10.4-267 §10.4 source ↗

Simplify Expressions by Applying Several Properties

In the following exercises, simplify.

$\frac{{(x^{3})}^{6}}{{(x^{4})}^{7}}$

Answer

\frac{1}{x^{10}}

10.4-269 §10.4 source ↗

Simplify Expressions by Applying Several Properties

In the following exercises, simplify.

${(\frac{2 r^{3}}{5 s})}^{4}$

Answer

\frac{16 r^{12}}{625 s^{4}}

10.4-271 §10.4 source ↗

Simplify Expressions by Applying Several Properties

In the following exercises, simplify.

${(\frac{3 y^{2} \cdot y^{5}}{y^{15} \cdot y^{8}})}^{0}$

Answer

10.4-273 §10.4 source ↗

Simplify Expressions by Applying Several Properties

In the following exercises, simplify.

$\frac{{(r^{2})}^{5} {(r^{4})}^{2}}{{(r^{3})}^{7}}$

Answer

\frac{1}{r^{3}}

10.4-275 §10.4 source ↗

Simplify Expressions by Applying Several Properties

In the following exercises, simplify.

$\frac{{(3 x^{4})}^{3} {(2 x^{3})}^{2}}{{(6 x^{5})}^{2}}$

Answer

3x⁸

10.4-277 §10.4 source ↗

Divide Monomials

In the following exercises, divide the monomials.

$48 b^{8} \div 6 b^{2}$

Answer

8b⁶

10.4-279 §10.4 source ↗

Divide Monomials

In the following exercises, divide the monomials.

$36 x^{3} \div (−2 x^{9})$

Answer

\frac{−18}{x^{6}}

10.4-281 §10.4 source ↗

Divide Monomials

In the following exercises, divide the monomials.

$\frac{18 x^{3}}{9 x^{2}}$

Answer

10.4-283 §10.4 source ↗

Divide Monomials

In the following exercises, divide the monomials.

$\frac{−35 x^{7}}{−42 x^{13}}$

Answer

\frac{5}{6 x^{6}}

10.4-285 §10.4 source ↗

Divide Monomials

In the following exercises, divide the monomials.

$\frac{18 r^{5} s}{3 r^{3} s^{9}}$

Answer

\frac{6 r^{2}}{s^{8}}

10.4-287 §10.4 source ↗

Divide Monomials

In the following exercises, divide the monomials.

$\frac{8 m n^{10}}{64 m n^{4}}$

Answer

\frac{n^{6}}{8}

10.4-289 §10.4 source ↗

Divide Monomials

In the following exercises, divide the monomials.

$\frac{−12 x^{4} y^{9}}{15 x^{6} y^{3}}$

Answer

- \frac{4 y^{6}}{5 x^{2}}

10.4-291 §10.4 source ↗

Divide Monomials

In the following exercises, divide the monomials.

$\frac{64 x^{5} y^{9} z^{7}}{48 x^{7} y^{12} z^{6}}$

Answer

\frac{4 z}{3 x^{2} y^{3}}

10.4-293 §10.4 source ↗

Divide Monomials

In the following exercises, divide the monomials.

$\frac{(6 m^{2} n) (5 m^{4} n^{3})}{3 m^{10} n^{2}}$

Answer

\frac{10 n^{2}}{m^{4}}

10.4-295 §10.4 source ↗

Divide Monomials

In the following exercises, divide the monomials.

$\frac{(4 u^{5} v^{4}) (15 u^{8} v)}{(12 u^{3} v) (u^{6} v)}$

Answer

5u⁴v³

10.4-297 §10.4 source ↗

Divide Monomials

In the following exercises, divide the monomials.

ⓐ $15 n^{10} + 3 n^{10}$

ⓑ $15 n^{10} - 3 n^{10}$

ⓓ $15 n^{10} \div 3 n^{10}$

Answer

ⓐ $18 n^{10}$

ⓑ $12 n^{10}$

ⓓ $5$

10.4-299 §10.4 source ↗

Divide Monomials

In the following exercises, divide the monomials.

ⓐ $q^{5} \cdot q^{3}$

ⓑ ${(q^{5})}^{3}$

Answer

ⓐ $q^{8}$

ⓑ $q^{15}$

10.4-301 §10.4 source ↗

Divide Monomials

In the following exercises, divide the monomials.

ⓐ $\frac{z^{6}}{z^{5}}$

ⓑ $\frac{z^{5}}{z^{6}}$

Answer

ⓐ $z$

ⓑ $\frac{1}{z}$

10.4-303 §10.4 source ↗

Divide Monomials

In the following exercises, divide the monomials.

$(4 y) (12 y^{7}) \div 8 y^{2}$

Answer

6 y^{6}

10.4-305 §10.4 source ↗

Divide Monomials

In the following exercises, divide the monomials.

$\frac{32 c^{11}}{4 c^{5}} +$ $\frac{42 c^{9}}{6 c^{3}}$

Answer

15 c^{6}

10.4-307 §10.4 source ↗

Divide Monomials

In the following exercises, divide the monomials.

$\frac{48 x^{6}}{6 x^{4}} -$ $\frac{35 x^{9}}{7 x^{7}}$

Answer

3 x^{2}

10.4-309 §10.4 source ↗

Divide Monomials

In the following exercises, divide the monomials.

$\frac{56 y^{4} z^{5}}{7 y^{3} z^{3}} -$ $\frac{45 y^{2} z^{2}}{5 y}$

Answer

- y z^{2}

10.4-311 §10.4 source ↗

Divide Monomials

In the following exercises, divide the monomials.

Memory One megabyte is approximately $10^{6}$ bytes. One terabyte is approximately $10^{12}$ bytes. How many megabytes are in one terabyte?

Answer

1,000,000

10.4-313 §10.4 source ↗

Divide Monomials

In the following exercises, divide the monomials.

Mai simplifies the quotient $\frac{y^{3}}{y}$ by writing $\frac{y^{3}}{y} = 3 .$ What is wrong with her reasoning?

Answer

Answers will vary.

10.4-315 §10.4 source ↗

Divide Monomials

In the following exercises, divide the monomials.

Roxie thinks $n^{0}$ simplifies to $0 .$ What would you say to convince Roxie she is wrong?

Answer

Answers will vary.

Be Prepared 10.12 §10.5 source ↗

What is the place value of the

6

in the number

64,891 ?

If you missed this problem, review Example 1.3.

Example 1.3 in the book ↗

Answer

ten thousand

Be Prepared 10.13 §10.5 source ↗

Name the decimal

0.0012 .

If you missed this problem, review Example 5.1.

Example 5.1 in the book ↗

Answer

twelve ten-thousandths

Be Prepared 10.14 §10.5 source ↗

Subtract:

5 - (−3) .

If you missed this problem, review Example 3.37.

Example 3.37 in the book ↗

Answer

8

Try It 10.125 §10.5 source ↗

Simplify:

ⓐ $2^{−3}$

ⓑ $10^{−2}$

Answer

ⓐ $\frac{1}{8}$

ⓑ $\frac{1}{100}$

Try It 10.126 §10.5 source ↗

Simplify:

ⓐ $3^{−2}$

ⓑ $10^{−4}$

Answer

ⓐ $\frac{1}{9}$

ⓑ $\frac{1}{10,000}$

Try It 10.127 §10.5 source ↗

Simplify:

ⓐ ${(−5)}^{−2}$

ⓑ $- 5^{−2}$

Answer

ⓐ $\frac{1}{25}$

ⓑ $- \frac{1}{25}$

Try It 10.128 §10.5 source ↗

Simplify:

ⓐ ${(−2)}^{−2}$

ⓑ ${−2}^{−2}$

Answer

ⓐ $\frac{1}{4}$

ⓑ $- \frac{1}{4}$

Try It 10.129 §10.5 source ↗

Simplify:

ⓐ $6 \cdot 3^{−1}$

ⓑ ${(6 \cdot 3)}^{−1}$

Answer

ⓐ $2$

ⓑ $\frac{1}{18}$

Try It 10.130 §10.5 source ↗

Simplify:

ⓐ $8 \cdot 2^{−2}$

ⓑ ${(8 \cdot 2)}^{−2}$

Answer

ⓐ $2$

ⓑ $\frac{1}{256}$

Try It 10.131 §10.5 source ↗

Simplify:

y^{−7} .

Answer

\frac{1}{y^{7}}

Try It 10.132 §10.5 source ↗

Simplify:

z^{−8} .

Answer

\frac{1}{z^{8}}

Try It 10.133 §10.5 source ↗

Simplify:

ⓐ $8 p^{−1}$

ⓑ ${(8 p)}^{−1}$

Answer

ⓐ $\frac{8}{p}$

ⓑ $\frac{1}{8 p}$

Try It 10.134 §10.5 source ↗

Simplify:

ⓐ $11 q^{−1}$

ⓑ ${(11 q)}^{−1}$

Answer

ⓐ $\frac{11}{q}$

ⓑ $\frac{1}{11 q}$

Try It 10.135 §10.5 source ↗

Simplify:

ⓐ $x^{−3} \cdot x^{7}$

ⓑ $y^{−7} \cdot y^{2}$

Answer

ⓐ $x^{4}$

ⓑ $\frac{1}{y^{5}}$

Try It 10.136 §10.5 source ↗

Simplify:

ⓐ $a^{−1} \cdot a^{6}$

ⓑ $b^{−8} \cdot b^{4}$

Answer

ⓐ $a^{5}$

ⓑ $\frac{1}{b^{4}}$

Try It 10.137 §10.5 source ↗

Simplify:

(p^{6} q^{−2}) (p^{−9} q^{−1}) .

Answer

\frac{1}{p^{3} q^{3}}

Try It 10.138 §10.5 source ↗

Simplify:

(r^{5} s^{−3}) (r^{−7} s^{−5}) .

Answer

\frac{1}{r^{2} s^{8}}

Try It 10.139 §10.5 source ↗

Simplify:

(3 u^{−5} v^{7}) (−4 u^{4} v^{−2}) .

Answer

- \frac{12 v^{5}}{u}

Try It 10.140 §10.5 source ↗

Simplify:

(−6 c^{−6} d^{4}) (−5 c^{−2} d^{−1}) .

Answer

\frac{30 d^{3}}{c^{8}}

Try It 10.141 §10.5 source ↗

Simplify:

{(x^{4})}^{−1} .

Answer

\frac{1}{x^{4}}

Try It 10.142 §10.5 source ↗

Simplify:

{(y^{2})}^{−2} .

Answer

\frac{1}{y^{4}}

Try It 10.143 §10.5 source ↗

Simplify:

{(8 a^{−4})}^{2} .

Answer

\frac{64}{a^{8}}

Try It 10.144 §10.5 source ↗

Simplify:

{(2 c^{−4})}^{3} .

Answer

\frac{8}{c^{12}}

Try It 10.145 §10.5 source ↗

Simplify:

\frac{x^{8}}{x^{−3}} .

Answer

x ¹¹

Try It 10.146 §10.5 source ↗

Simplify:

\frac{y^{7}}{y^{−6}} .

Answer

y ¹³

Try It 10.147 §10.5 source ↗

Write in scientific notation:

96,000 .

Answer

9.6 × 10⁴

Try It 10.148 §10.5 source ↗

Write in scientific notation:

48,300 .

Answer

4.83 × 10⁴

Try It 10.149 §10.5 source ↗

Write in scientific notation:

0.0078 .

Answer

7.8 × 10⁻³

Try It 10.150 §10.5 source ↗

Write in scientific notation:

0.0129 .

Answer

1.29 × 10⁻²

Try It 10.151 §10.5 source ↗

Convert to decimal form:

1.3 \times 10^{3} .

Answer

1,300

Try It 10.152 §10.5 source ↗

Convert to decimal form:

9.25 \times 10^{4} .

Answer

92,500

Try It 10.153 §10.5 source ↗

Convert to decimal form:

1.2 \times 10^{−4} .

Answer

0.00012

Try It 10.154 §10.5 source ↗

Convert to decimal form:

7.5 \times 10^{−2} .

Answer

0.075

Try It 10.155 §10.5 source ↗

Multiply. Write answers in decimal form:

(3 \times 10^{6}) (2 \times 10^{−8}) .

Answer

0.06

Try It 10.156 §10.5 source ↗

Multiply. Write answers in decimal form:

(3 \times 10^{−2}) (3 \times 10^{−1}) .

Answer

0.009

Try It 10.157 §10.5 source ↗

Divide. Write answers in decimal form:

\frac{8 \times 10^{4}}{2 \times 10^{−1}} .

Answer

400,000

Try It 10.158 §10.5 source ↗

Divide. Write answers in decimal form:

\frac{8 \times 10^{2}}{4 \times 10^{−2}} .

Answer

20,000

10.5-317 §10.5 source ↗

Use the Definition of a Negative Exponent

In the following exercises, simplify.

$8^{−2}$

Answer

\frac{1}{64}

10.5-319 §10.5 source ↗

Use the Definition of a Negative Exponent

In the following exercises, simplify.

$2^{−5}$

Answer

\frac{1}{32}

10.5-321 §10.5 source ↗

Use the Definition of a Negative Exponent

In the following exercises, simplify.

$10^{−1}$

Answer

\frac{1}{10}

10.5-323 §10.5 source ↗

Use the Definition of a Negative Exponent

In the following exercises, simplify.

$3^{−2} + 3^{−1}$

Answer

\frac{4}{9}

10.5-325 §10.5 source ↗

Use the Definition of a Negative Exponent

In the following exercises, simplify.

$10^{−1} + 2^{−1}$

Answer

\frac{3}{5}

10.5-327 §10.5 source ↗

Use the Definition of a Negative Exponent

In the following exercises, simplify.

$2^{0} - 2^{−1} + 2^{−2}$

Answer

\frac{3}{4}

10.5-329 §10.5 source ↗

Use the Definition of a Negative Exponent

In the following exercises, simplify.

ⓐ ${(−8)}^{−2}$

ⓑ $- 8^{−2}$

Answer

ⓐ $\frac{1}{64}$

ⓑ $- \frac{1}{64}$

10.5-331 §10.5 source ↗

Use the Definition of a Negative Exponent

In the following exercises, simplify.

ⓐ ${(−4)}^{−6}$

ⓑ $- 4^{−6}$

Answer

ⓐ $\frac{1}{4096}$

ⓑ $- \frac{1}{4096}$

10.5-333 §10.5 source ↗

Use the Definition of a Negative Exponent

In the following exercises, simplify.

ⓐ $10 \cdot 3^{−1}$

ⓑ ${(10 \cdot 3)}^{−1}$

Answer

ⓐ $\frac{10}{3}$

ⓑ $\frac{1}{30}$

10.5-335 §10.5 source ↗

Use the Definition of a Negative Exponent

In the following exercises, simplify.

ⓐ $3 \cdot 5^{−2}$

ⓑ ${(3 \cdot 5)}^{−2}$

Answer

ⓐ $\frac{3}{25}$

ⓑ $\frac{1}{225}$

10.5-337 §10.5 source ↗

Use the Definition of a Negative Exponent

In the following exercises, simplify.

$p^{−3}$

Answer

\frac{1}{p^{3}}

10.5-339 §10.5 source ↗

Use the Definition of a Negative Exponent

In the following exercises, simplify.

$m^{−5}$

Answer

\frac{1}{m^{5}}

10.5-341 §10.5 source ↗

Use the Definition of a Negative Exponent

In the following exercises, simplify.

ⓐ $3 q^{−1}$

ⓑ ${(3 q)}^{−1}$

Answer

ⓐ $\frac{3}{q}$

ⓑ $\frac{1}{3 q}$

10.5-343 §10.5 source ↗

Use the Definition of a Negative Exponent

In the following exercises, simplify.

ⓐ $10 k^{−1}$

ⓑ ${(10 k)}^{−1}$

Answer

ⓐ $\frac{10}{k}$

ⓑ $\frac{1}{10 k}$

10.5-345 §10.5 source ↗

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

$r^{−2} \cdot r^{5}$

Answer

r ³

10.5-347 §10.5 source ↗

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

$q^{−8} \cdot q^{3}$

Answer

\frac{1}{q^{5}}

10.5-349 §10.5 source ↗

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

$z^{−6} \cdot z^{−2}$

Answer

\frac{1}{z^{8}}

10.5-351 §10.5 source ↗

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

$m \cdot m^{−2}$

Answer

\frac{1}{m}

10.5-353 §10.5 source ↗

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

$x^{4} \cdot x^{−2} \cdot x^{−3}$

Answer

\frac{1}{x}

10.5-355 §10.5 source ↗

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

$u^{2} v^{−2}$

Answer

\frac{u^{2}}{v^{2}}

10.5-357 §10.5 source ↗

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

$(a^{3} b^{−3}) (a^{−5} b^{−1})$

Answer

\frac{1}{a^{2} b^{4}}

10.5-359 §10.5 source ↗

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

$(p q^{−4}) (p^{−6} q^{−3})$

Answer

\frac{1}{p^{5} q^{7}}

10.5-361 §10.5 source ↗

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

$(−3 p^{−5} q^{8}) (7 p^{2} q^{−3})$

Answer

- \frac{21 q^{5}}{p^{3}}

10.5-363 §10.5 source ↗

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

$(−8 a^{−5} b^{−4}) (−4 a^{2} b^{3})$

Answer

\frac{32}{a^{3} b}

10.5-365 §10.5 source ↗

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

${(q^{10})}^{−10}$

Answer

\frac{1}{q^{100}}

10.5-367 §10.5 source ↗

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

${(x^{4})}^{−1}$

Answer

\frac{1}{x^{4}}

10.5-369 §10.5 source ↗

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

${(p^{−3})}^{2}$

Answer

\frac{1}{p^{6}}

10.5-371 §10.5 source ↗

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

${(m^{−2})}^{−3}$

Answer

m ⁶

10.5-373 §10.5 source ↗

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

${(3 q^{−5})}^{2}$

Answer

\frac{9}{q^{10}}

10.5-375 §10.5 source ↗

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

${(2 n^{−3})}^{−6}$

Answer

\frac{n^{18}}{64}

10.5-377 §10.5 source ↗

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

$\frac{b^{5}}{b^{−3}}$

Answer

b ⁸

10.5-379 §10.5 source ↗

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

$\frac{m^{5}}{m^{−2}}$

Answer

m ⁷

10.5-381 §10.5 source ↗

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

$\frac{r^{6}}{r^{9}}$

Answer

\frac{1}{r^{3}}

10.5-383 §10.5 source ↗

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

$\frac{p^{−3}}{p^{−6}}$

Answer

p ³

10.5-385 §10.5 source ↗

Convert from Decimal Notation to Scientific Notation

In the following exercises, write each number in scientific notation.

280,000

Answer

2.8 × 10⁵

10.5-387 §10.5 source ↗

Convert from Decimal Notation to Scientific Notation

In the following exercises, write each number in scientific notation.

1,290,000

Answer

1.29 × 10⁶

10.5-389 §10.5 source ↗

Convert from Decimal Notation to Scientific Notation

In the following exercises, write each number in scientific notation.

0.041

Answer

4.1 × 10⁻²

10.5-391 §10.5 source ↗

Convert from Decimal Notation to Scientific Notation

In the following exercises, write each number in scientific notation.

0.0000103

Answer

1.03 × 10⁻⁵

10.5-393 §10.5 source ↗

Convert from Decimal Notation to Scientific Notation

In the following exercises, write each number in scientific notation.

The population of the world on July 4, 2010 was more than $6,850,000,000 .$

Answer

6.85 × 10⁹

10.5-395 §10.5 source ↗

Convert from Decimal Notation to Scientific Notation

In the following exercises, write each number in scientific notation.

The probability of winning the $2010$ Megamillions lottery is about $0.0000000057 .$

Answer

5.7 × 10⁻⁹

10.5-397 §10.5 source ↗

Convert Scientific Notation to Decimal Form

In the following exercises, convert each number to decimal form.

$8.3 \times 10^{2}$

Answer

830

10.5-399 §10.5 source ↗

Convert Scientific Notation to Decimal Form

In the following exercises, convert each number to decimal form.

$1.6 \times 10^{10}$

Answer

16,000,000,000

10.5-401 §10.5 source ↗

Convert Scientific Notation to Decimal Form

In the following exercises, convert each number to decimal form.

$2.8 \times 10^{−2}$

Answer

0.028

10.5-403 §10.5 source ↗

Convert Scientific Notation to Decimal Form

In the following exercises, convert each number to decimal form.

$6.15 \times 10^{−8}$

Answer

0.0000000615

10.5-405 §10.5 source ↗

Convert Scientific Notation to Decimal Form

In the following exercises, convert each number to decimal form.

At the start of 2012, the US federal budget had a deficit of more than $$1.5 \times 10^{13} .$

Answer

$15,000,000,000,000

10.5-407 §10.5 source ↗

Convert Scientific Notation to Decimal Form

In the following exercises, convert each number to decimal form.

The width of a proton is $1 \times 10^{−5}$ of the width of an atom.

Answer

0.00001

10.5-409 §10.5 source ↗

Multiply and Divide Using Scientific Notation

In the following exercises, multiply or divide and write your answer in decimal form.

$(3 \times 10^{2}) (1 \times 10^{−5})$

Answer

0.003

10.5-411 §10.5 source ↗

Multiply and Divide Using Scientific Notation

In the following exercises, multiply or divide and write your answer in decimal form.

$(2.1 \times 10^{−4}) (3.5 \times 10^{−2})$

Answer

0.00000735

10.5-413 §10.5 source ↗

Multiply and Divide Using Scientific Notation

In the following exercises, multiply or divide and write your answer in decimal form.

$\frac{8 \times 10^{6}}{4 \times 10^{−1}}$

Answer

20,000,000

10.5-415 §10.5 source ↗

Multiply and Divide Using Scientific Notation

In the following exercises, multiply or divide and write your answer in decimal form.

$\frac{5 \times 10^{−3}}{1 \times 10^{−10}}$

Answer

50,000,000

10.5-417 §10.5 source ↗

Multiply and Divide Using Scientific Notation

In the following exercises, multiply or divide and write your answer in decimal form.

Length of a year The difference between the calendar year and the astronomical year is $0.000125$ day.

ⓐ Write this number in scientific notation.

ⓑ How many years does it take for the difference to become 1 day?

Answer

ⓐ 1.25 × 10⁻⁴

ⓐ 8,000

10.5-419 §10.5 source ↗

Multiply and Divide Using Scientific Notation

In the following exercises, multiply or divide and write your answer in decimal form.

Calculator display Many calculators automatically show answers in scientific notation if there are more digits than can fit in the calculator’s display. To find the number of ways Barbara could make a collage with $6$ of her $50$ favorite photographs, she multiplied $50 \cdot 49 \cdot 48 \cdot 47 \cdot 46 \cdot 45 .$ Her calculator gave the answer $1.1441304 \times 10^{10} .$ Write the number in decimal notation.

Answer

11,441,304,000

10.5-421 §10.5 source ↗

Multiply and Divide Using Scientific Notation

In the following exercises, multiply or divide and write your answer in decimal form.

When you convert a number from decimal notation to scientific notation, how do you know if the exponent will be positive or negative?

Answer

Answers will vary.

Be Prepared 10.15 §10.6 source ↗

Factor

56

into primes.
If you missed this problem, review Example 2.48.

Example 2.48 in the book ↗

Answer

2 \cdot 2 \cdot 2 \cdot 7

Be Prepared 10.16 §10.6 source ↗

Multiply:

−3 (6 a + 11) .

If you missed this problem, review Example 7.25.

Example 7.25 in the book ↗

Answer

- 18 a - 33

Be Prepared 10.17 §10.6 source ↗

Multiply:

4 x^{2} (x^{2} + 3 x - 1) .

If you missed this problem, review Example 10.32.

Example 10.32 in the book ↗

Answer

4 x^{4} +

12 x^{3} -

4 x^{2}

Try It 10.159 §10.6 source ↗

Find the greatest common factor:

54, 36 .

Answer

Try It 10.160 §10.6 source ↗

Find the greatest common factor:

48, 80 .

Answer

Try It 10.161 §10.6 source ↗

Find the greatest common factor:

7 y, 14 .

Answer

Try It 10.162 §10.6 source ↗

Find the greatest common factor:

22, 11 m .

Answer

Try It 10.163 §10.6 source ↗

Find the greatest common factor:

16 x^{2}, 24 x^{3} .

Answer

8x²

Try It 10.164 §10.6 source ↗

Find the greatest common factor:

27 y^{3}, 18 y^{4} .

Answer

9y³

Try It 10.165 §10.6 source ↗

Find the greatest common factor:

21 x^{3},

9 x^{2},

15 x .

Answer

Try It 10.166 §10.6 source ↗

Find the greatest common factor:

25 m^{4},

35 m^{3},

20 m^{2} .

Answer

5m²

Try It 10.167 §10.6 source ↗

Factor:

4 x + 12 .

Answer

4(x + 3)

Try It 10.168 §10.6 source ↗

Factor:

6 a + 24 .

Answer

6(a + 4)

Try It 10.169 §10.6 source ↗

Factor:

9 a + 9 .

Answer

9(a + 1)

Try It 10.170 §10.6 source ↗

Factor:

11 x + 11 .

Answer

11(x + 1)

Try It 10.171 §10.6 source ↗

Factor:

11 x - 44 .

Answer

11(x − 4)

Try It 10.172 §10.6 source ↗

Factor:

13 y - 52 .

Answer

13(y − 4)

Try It 10.173 §10.6 source ↗

Factor:

4 y^{2} + 8 y + 12 .

Answer

4(y² + 2y + 3)

Try It 10.174 §10.6 source ↗

Factor:

6 x^{2} + 42 x - 12 .

Answer

6(x² + 7x − 2)

Try It 10.175 §10.6 source ↗

Factor:

9 x^{2} + 7 x .

Answer

x(9x + 7)

Try It 10.176 §10.6 source ↗

Factor:

5 a^{2} - 12 a .

Answer

a(5a − 12)

Try It 10.177 §10.6 source ↗

Factor:

2 x^{3} + 12 x^{2} .

Answer

2x²(x + 6)

Try It 10.178 §10.6 source ↗

Factor:

6 y^{3} - 15 y^{2} .

Answer

3y²(2y − 5)

Try It 10.179 §10.6 source ↗

Factor:

18 y^{2} + 63 y .

Answer

9y(2y + 7)

Try It 10.180 §10.6 source ↗

Factor:

32 k^{2} + 56 k .

Answer

8k(4k + 7)

Try It 10.181 §10.6 source ↗

Factor:

18 y^{3} -

6 y^{2} -

24 y .

Answer

6y(3y² − y − 4)

Try It 10.182 §10.6 source ↗

Factor:

16 x^{3} +

8 x^{2} -

12 x .

Answer

4x(4x² + 2x − 3)

Try It 10.183 §10.6 source ↗

Factor:

−5 y - 35 .

Answer

−5(y + 7)

Try It 10.184 §10.6 source ↗

Factor:

−16 z - 56 .

Answer

−8(2z + 7)

Try It 10.185 §10.6 source ↗

Factor:

−7 a^{2} + 21 a .

Answer

−7a(a − 3)

Try It 10.186 §10.6 source ↗

Factor:

−6 x^{2} + x .

Answer

−x(6x − 1)

10.6-423 §10.6 source ↗

Find the Greatest Common Factor of Two or More Expressions

In the following exercises, find the greatest common factor.

$45, 75$

Answer

10.6-425 §10.6 source ↗

Find the Greatest Common Factor of Two or More Expressions

In the following exercises, find the greatest common factor.

$150, 275$

Answer

10.6-427 §10.6 source ↗

Find the Greatest Common Factor of Two or More Expressions

In the following exercises, find the greatest common factor.

$4 y, 28$

Answer

10.6-429 §10.6 source ↗

Find the Greatest Common Factor of Two or More Expressions

In the following exercises, find the greatest common factor.

$5 b, 30$

Answer

10.6-431 §10.6 source ↗

Find the Greatest Common Factor of Two or More Expressions

In the following exercises, find the greatest common factor.

$9 x, 15 x^{2}$

Answer

10.6-433 §10.6 source ↗

Find the Greatest Common Factor of Two or More Expressions

In the following exercises, find the greatest common factor.

$12 p^{4}, 48 p^{3}$

Answer

12p³

10.6-435 §10.6 source ↗

Find the Greatest Common Factor of Two or More Expressions

In the following exercises, find the greatest common factor.

$18 a,$ $6 a^{2},$ $22 a^{3}$

Answer

10.6-437 §10.6 source ↗

Find the Greatest Common Factor of Two or More Expressions

In the following exercises, find the greatest common factor.

$40 y,$ $10 y^{2},$ $90 y^{3}$

Answer

10y

10.6-439 §10.6 source ↗

Find the Greatest Common Factor of Two or More Expressions

In the following exercises, find the greatest common factor.

$35 x^{3},$ $10 x^{4},$ $5 x^{5}$

Answer

5x³

10.6-441 §10.6 source ↗

Find the Greatest Common Factor of Two or More Expressions

In the following exercises, find the greatest common factor.

$14 b^{2},$ $35 b^{3},$ $63 b^{4}$

Answer

7b²

10.6-443 §10.6 source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

$5 y + 15$

Answer

5(y + 3)

10.6-445 §10.6 source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

$4 b - 20$

Answer

4(b − 5)

10.6-447 §10.6 source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

$7 x - 7$

Answer

7(x − 1)

10.6-449 §10.6 source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

$3 n^{2} + 21 n + 12$

Answer

3(n² + 7n + 4)

10.6-451 §10.6 source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

$6 q^{2} + 30 q + 42$

Answer

6(q² + 5q + 7)

10.6-453 §10.6 source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

$9 c^{2} + 22 c$

Answer

c(9c + 22)

10.6-455 §10.6 source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

$17 x^{2} + 7 x$

Answer

x(17x + 7)

10.6-457 §10.6 source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

$4 q^{2} + 7 q$

Answer

q(4q + 7)

10.6-459 §10.6 source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

$3 r^{2} + 27 r$

Answer

3r(r + 9)

10.6-461 §10.6 source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

$30 u^{2} - 10 u$

Answer

10u(3u − 1)

10.6-463 §10.6 source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

$a b + 8 b$

Answer

b(a + 8)

10.6-465 §10.6 source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

$55 y - 11 y^{4}$

Answer

11y(5 − y³)

10.6-467 §10.6 source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

$45 c^{3} - 15 c^{2}$

Answer

15c²(3c − 1)

10.6-469 §10.6 source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

$6 c^{3} - 6 c d^{2}$

Answer

6c(c² − d²)

10.6-471 §10.6 source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

$48 x^{3} + 72 x^{2}$

Answer

24x²(2x + 3)

10.6-473 §10.6 source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

$144 a^{6} + 90 a^{3}$

Answer

18a³(8a³ + 5)

10.6-475 §10.6 source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

$10 y^{2} + 50 y + 40$

Answer

10(y² + 5y + 4)

10.6-477 §10.6 source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

$12 u^{2} -$ $36 u -$ $108$

Answer

12(u² − 3u − 9)

10.6-479 §10.6 source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

$5 p^{4} -$ $20 p^{3} -$ $15 p^{2}$

Answer

5p²(p² − 4p − 3)

10.6-481 §10.6 source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

$8 c^{5} +$ $40 c^{4} -$ $56 c^{3}$

Answer

8c³(c² + 5c − 7)

10.6-483 §10.6 source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

$−7 p - 84$

Answer

−7(p + 12)

10.6-485 §10.6 source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

$−18 b^{2} - 66 b$

Answer

−6b(3b + 11)

10.6-487 §10.6 source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

$−8 a^{3} + 32 a^{2}$

Answer

−8a²(a − 4)

10.6-489 §10.6 source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

$−9 b^{5} + 63 b^{3}$

Answer

−9b³(b² − 7)

10.6-491 §10.6 source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

Height of a baseball The height of a baseball hit with velocity $80$ feet/second at $4$ feet above ground level is $−16 t^{2} +$ $80 t +$ $4,$ with $t =$ the number of seconds since it was hit. Factor the greatest common factor from this polynomial.

Answer

−4(4t² − 20t − 1)

10.6-493 §10.6 source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

What is the GCF of $y^{4}$ , $y^{5}$ , and $y^{10}$ ? Write a general rule that tells how to find the GCF of $y^{a}$ , $y^{b}$ , and $y^{c}$ .

Answer

Answers will vary.

10.R-494 §10.R source ↗

Identify Polynomials, Monomials, Binomials and Trinomials

In the following exercises, determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial.

$y^{2} + 8 y - 20$

Answer

trinomial

10.R-496 §10.R source ↗

Identify Polynomials, Monomials, Binomials and Trinomials

In the following exercises, determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial.

$9 x^{3} - 1$

Answer

binomial

10.R-498 §10.R source ↗

Determine the Degree of Polynomials

In the following exercises, determine the degree of each polynomial.

$16 x^{2} - 40 x - 25$

Answer

10.R-500 §10.R source ↗

Determine the Degree of Polynomials

In the following exercises, determine the degree of each polynomial.

$−15$

Answer

10.R-502 §10.R source ↗

Add and Subtract Monomials

In the following exercises, add or subtract the monomials.

$4 p + 11 p$

Answer

15p

10.R-504 §10.R source ↗

Add and Subtract Monomials

In the following exercises, add or subtract the monomials.

Add $4 n^{5},$ $− n^{5},$ $−6 n^{5}$

Answer

−3n⁵

10.R-506 §10.R source ↗

Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

$(4 a^{2} + 9 a - 11) +$ $(6 a^{2} - 5 a + 10)$

Answer

10a² + 4a − 1

10.R-508 §10.R source ↗

Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

$(y^{2} - 3 y + 12) +$ $(5 y^{2} - 9)$

Answer

6y² − 3y + 3

10.R-510 §10.R source ↗

Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

Find the sum of $8 q^{3} - 27$ and $q^{2} + 6 q - 2$

Answer

8q³ + q² + 6q − 29

10.R-512 §10.R source ↗

Evaluate a Polynomial for a Given Value of the Variable

In the following exercises, evaluate each polynomial for the given value.

$200 x - \frac{1}{5} x^{2}$ when $x = 5$

Answer

995

10.R-514 §10.R source ↗

Evaluate a Polynomial for a Given Value of the Variable

In the following exercises, evaluate each polynomial for the given value.

$200 x - \frac{1}{5} x^{2}$ when $x = 15$

Answer

2,955

10.R-516 §10.R source ↗

Evaluate a Polynomial for a Given Value of the Variable

In the following exercises, evaluate each polynomial for the given value.

$5 + 40 x - \frac{1}{2} x^{2}$ when $x = −4$

Answer

−163

10.R-518 §10.R source ↗

Evaluate a Polynomial for a Given Value of the Variable

In the following exercises, evaluate each polynomial for the given value.

A pair of glasses is dropped off a bridge $640$ feet above a river. The polynomial $−16 t^{2} + 640$ gives the height of the glasses $t$ seconds after they were dropped. Find the height of the glasses when $t = 6 .$

Answer

64 feet

10.R-520 §10.R source ↗

Simplify Expressions with Exponents

In the following exercises, simplify.

$6^{3}$

Answer

216

10.R-522 §10.R source ↗

Simplify Expressions with Exponents

In the following exercises, simplify.

${(−0.5)}^{2}$

Answer

0.25

10.R-524 §10.R source ↗

Simplify Expressions Using the Product Property of Exponents

In the following exercises, simplify each expression.

$p^{3} \cdot p^{10}$

Answer

p ¹³

10.R-526 §10.R source ↗

Simplify Expressions Using the Product Property of Exponents

In the following exercises, simplify each expression.

$a \cdot a^{2} \cdot a^{3}$

Answer

a ⁶

10.R-528 §10.R source ↗

Simplify Expressions Using the Power Property of Exponents

In the following exercises, simplify each expression.

${(y^{4})}^{3}$

Answer

y ¹²

10.R-530 §10.R source ↗

Simplify Expressions Using the Power Property of Exponents

In the following exercises, simplify each expression.

${(3^{2})}^{5}$

Answer

3¹⁰

10.R-532 §10.R source ↗

Simplify Expressions Using the Product to a Power Property

In the following exercises, simplify each expression.

${(8 n)}^{2}$

Answer

64n²

10.R-534 §10.R source ↗

Simplify Expressions Using the Product to a Power Property

In the following exercises, simplify each expression.

${(2 a b)}^{8}$

Answer

256a⁸b⁸

10.R-536 §10.R source ↗

Simplify Expressions by Applying Several Properties

In the following exercises, simplify each expression.

${(3 a^{5})}^{3}$

Answer

27a¹⁵

10.R-538 §10.R source ↗

Simplify Expressions by Applying Several Properties

In the following exercises, simplify each expression.

${(x^{3})}^{5} {(x^{2})}^{3}$

Answer

x ²¹

10.R-540 §10.R source ↗

Multiply Monomials

In the following exercises, multiply the monomials.

$(−6 p^{4}) (9 p)$

Answer

−54p⁵

10.R-542 §10.R source ↗

Multiply Monomials

In the following exercises, multiply the monomials.

$(8 x^{2} y^{5}) (7 x y^{6})$

Answer

56x³y¹¹

10.R-544 §10.R source ↗

Multiply a Polynomial by a Monomial

In the following exercises, multiply.

$7 (10 - x)$

Answer

70 − 7x

10.R-546 §10.R source ↗

Multiply a Polynomial by a Monomial

In the following exercises, multiply.

$−5 y (125 y^{3} - 1)$

Answer

−625y⁴ + 5y

10.R-548 §10.R source ↗

Multiply a Binomial by a Binomial

In the following exercises, multiply the binomials using various methods.

$(a + 5) (a + 2)$

Answer

a² + 7a + 10

10.R-550 §10.R source ↗

Multiply a Binomial by a Binomial

In the following exercises, multiply the binomials using various methods.

$(3 x + 1) (2 x - 7)$

Answer

6x² − 19x − 7

10.R-552 §10.R source ↗

Multiply a Binomial by a Binomial

In the following exercises, multiply the binomials using various methods.

$(n + 8) (n + 1)$

Answer

n² + 9n + 8

10.R-554 §10.R source ↗

Multiply a Binomial by a Binomial

In the following exercises, multiply the binomials using various methods.

$(5 u - 3) (u + 8)$

Answer

5u² + 37u − 24

10.R-556 §10.R source ↗

Multiply a Binomial by a Binomial

In the following exercises, multiply the binomials using various methods.

$(p + 4) (p + 7)$

Answer

p² + 11p + 28

10.R-558 §10.R source ↗

Multiply a Binomial by a Binomial

In the following exercises, multiply the binomials using various methods.

$(3 c + 1) (9 c - 4)$

Answer

27c² − 3c − 4

10.R-560 §10.R source ↗

Multiply a Trinomial by a Binomial

In the following exercises, multiply using any method.

$(x + 1) (x^{2} - 3 x - 21)$

Answer

x³ − 2x² − 24x − 21

10.R-562 §10.R source ↗

Multiply a Trinomial by a Binomial

In the following exercises, multiply using any method.

$(m + 6) (m^{2} - 7 m - 30)$

Answer

m³ − m² − 72m − 180

10.R-564 §10.R source ↗

Simplify Expressions Using the Quotient Property of Exponents

In the following exercises, simplify.

$\frac{2^{8}}{2^{2}}$

Answer

2⁶ or 64

10.R-566 §10.R source ↗

Simplify Expressions Using the Quotient Property of Exponents

In the following exercises, simplify.

$\frac{n^{3}}{n^{12}}$

Answer

\frac{1}{n^{9}}

10.R-568 §10.R source ↗

Simplify Expressions with Zero Exponents

In the following exercises, simplify.

$3^{0}$

Answer

10.R-570 §10.R source ↗

Simplify Expressions with Zero Exponents

In the following exercises, simplify.

${(14 t)}^{0}$

Answer

10.R-572 §10.R source ↗

Simplify Expressions Using the Quotient to a Power Property

In the following exercises, simplify.

${(\frac{3}{5})}^{2}$

Answer

\frac{9}{25}

10.R-574 §10.R source ↗

Simplify Expressions Using the Quotient to a Power Property

In the following exercises, simplify.

${(\frac{5 m}{n})}^{3}$

Answer

\frac{125 m^{3}}{n^{3}}

10.R-576 §10.R source ↗

Simplify Expressions by Applying Several Properties

In the following exercises, simplify.

$\frac{{(a^{3})}^{2}}{a^{4}}$

Answer

a ²

10.R-578 §10.R source ↗

Simplify Expressions by Applying Several Properties

In the following exercises, simplify.

${(\frac{x}{x^{9}})}^{5}$

Answer

\frac{1}{x^{40}}

10.R-580 §10.R source ↗

Simplify Expressions by Applying Several Properties

In the following exercises, simplify.

$\frac{{(n^{5})}^{3}}{{(n^{2})}^{8}}$

Answer

\frac{1}{n}

10.R-582 §10.R source ↗

Divide Monomials

In the following exercises, divide the monomials.

$72 p^{12} \div 8 p^{3}$

Answer

9p⁹

10.R-584 §10.R source ↗

Divide Monomials

In the following exercises, divide the monomials.

$\frac{45 y^{6}}{−15 y^{10}}$

Answer

- \frac{3}{y^{4}}

10.R-586 §10.R source ↗

Divide Monomials

In the following exercises, divide the monomials.

$\frac{28 a^{9} b}{7 a^{4} b^{3}}$

Answer

\frac{4 a^{5}}{b^{2}}

10.R-588 §10.R source ↗

Divide Monomials

In the following exercises, divide the monomials.

$\frac{(5 m^{9} n^{3}) (8 m^{3} n^{2})}{(10 m n^{4}) (m^{2} n^{5})}$

Answer

\frac{4 m^{9}}{n^{4}}

10.R-590 §10.R source ↗

Use the Definition of a Negative Exponent

In the following exercises, simplify.

$6^{−2}$

Answer

\frac{1}{36}

10.R-592 §10.R source ↗

Use the Definition of a Negative Exponent

In the following exercises, simplify.

$5 \cdot 2^{−4}$

Answer

\frac{5}{16}

10.R-594 §10.R source ↗

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

$x^{−3} \cdot x^{9}$

Answer

x ⁶

10.R-596 §10.R source ↗

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

$(u v^{−3}) (u^{−4} v^{−2})$

Answer

\frac{1}{u^{3} v^{5}}

10.R-598 §10.R source ↗

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

${(k^{−2})}^{−3}$

Answer

k ⁶

10.R-600 §10.R source ↗

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

$\frac{b^{8}}{b^{−2}}$

Answer

b ¹⁰

10.R-602 §10.R source ↗

Convert from Decimal Notation to Scientific Notation

In the following exercises, write each number in scientific notation.

$5,300,000$

Answer

5.3 × 10⁶

10.R-604 §10.R source ↗

Convert from Decimal Notation to Scientific Notation

In the following exercises, write each number in scientific notation.

The thickness of a piece of paper is about $0.097$ millimeter.

Answer

9.7 × 10⁻² millimeter

10.R-606 §10.R source ↗

Convert Scientific Notation to Decimal Form

In the following exercises, convert each number to decimal form.

$2.9 \times 10^{4}$

Answer

29,000

10.R-608 §10.R source ↗

Convert Scientific Notation to Decimal Form

In the following exercises, convert each number to decimal form.

$3.75 \times 10^{−1}$

Answer

0.375

10.R-610 §10.R source ↗

Multiply and Divide Using Scientific Notation

In the following exercises, multiply and write your answer in decimal form.

$(3 \times 10^{7}) (2 \times 10^{−4})$

Answer

6,000

10.R-612 §10.R source ↗

Multiply and Divide Using Scientific Notation

In the following exercises, multiply and write your answer in decimal form.

$\frac{6 \times 10^{9}}{2 \times 10^{−1}}$

Answer

30,000,000,000

10.R-614 §10.R source ↗

Find the Greatest Common Factor of Two or More Expressions

In the following exercises, find the greatest common factor.

$5 n, 45$

Answer

10.R-616 §10.R source ↗

Find the Greatest Common Factor of Two or More Expressions

In the following exercises, find the greatest common factor.

$12 x^{2},$ $20 x^{3},$ $36 x^{4}$

Answer

4x²

10.R-618 §10.R source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

$16 u - 24$

Answer

8(2u − 3)

10.R-620 §10.R source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

$6 p^{2} + 6 p$

Answer

6p(p + 1)

10.R-622 §10.R source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

$−9 a^{5} - 9 a^{3}$

Answer

−9a³(a² + 1)

10.R-624 §10.R source ↗

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

$5 y^{2} - 55 y + 45$

Answer

5(y² − 11y + 9)

10.T-626 §10.T source ↗

For the polynomial $8 y^{4} - 3 y^{2} + 1$

ⓐ Is it a monomial, binomial, or trinomial?

ⓑ What is its degree?

Answer

ⓐ trinomial

ⓑ 4

10.T-628 §10.T source ↗

In the following exercises, simplify each expression.

$(10 x^{2} - 3 x + 5) -$ $(4 x^{2} - 6)$

Answer

6x² − 3x + 11

10.T-630 §10.T source ↗

In the following exercises, simplify each expression.

$n \cdot n^{4}$

Answer

n ⁵

10.T-632 §10.T source ↗

In the following exercises, simplify each expression.

$(8 x y^{3}) (−6 x^{4} y^{6})$

Answer

−48x⁵y⁹

10.T-634 §10.T source ↗

In the following exercises, simplify each expression.

$(s + 8) (s + 9)$

Answer

s² + 17s + 72

10.T-636 §10.T source ↗

In the following exercises, simplify each expression.

$(11 a - 6) (5 a - 1)$

Answer

55a² − 41a + 6

10.T-638 §10.T source ↗

In the following exercises, simplify each expression.

$(4 a + 9 b) (6 a - 5 b)$

Answer

24a² + 34ab − 45b²

10.T-640 §10.T source ↗

In the following exercises, simplify each expression.

${(\frac{x^{3} \cdot x^{9}}{x^{5}})}^{2}$

Answer

x ¹⁴

10.T-642 §10.T source ↗

In the following exercises, simplify each expression.

$\frac{24 r^{3} s}{6 r^{2} s^{7}}$

Answer

\frac{4 r}{s^{6}}

10.T-644 §10.T source ↗

In the following exercises, simplify each expression.

$(15 x y^{3} - 35 x^{2} y) \div 5 x y$

Answer

3y² − 7x

10.T-646 §10.T source ↗

In the following exercises, simplify each expression.

${(2 y)}^{−3}$

Answer

\frac{1}{8 y^{3}}

10.T-648 §10.T source ↗

In the following exercises, simplify each expression.

$\frac{x^{4}}{x^{−5}}$

Answer

x ⁹

10.T-650 §10.T source ↗

In the following exercises, factor the greatest common factor from each polynomial.

$−6 x^{2} - 30 x$

Answer

−6x(x + 5)

10.T-652 §10.T source ↗

In the following exercises, factor the greatest common factor from each polynomial.

Convert $5.25 \times 10^{−4}$ to decimal form.

Answer

0.000525

10.T-654 §10.T source ↗

In the following exercises, simplify, and write your answer in decimal form.

$\frac{9 \times 10^{4}}{3 \times 10^{−1}}$

Answer

300,000

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Problems and answers are adapted from Prealgebra 2e by Lynn Marecek, MaryAnne Anthony-Smith and Andrea Honeycutt Mathis, OpenStax, and are used under the CC BY-NC-SA 4.0 licence. Access for free at https://openstax.org/books/prealgebra-2e/pages/1-introduction. Illustrations: Copyright Rice University, OpenStax, under CC BY-NC-SA 4.0 license. This adaptation is released under the same licence, is non-commercial, and is neither affiliated with nor endorsed by OpenStax or Rice University.