Q 549. In the following exercises, simp... [FREE SOLUTION]

91影视

Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 9: Q 549. (page 1143)

In the following exercises, simplify.
(a) ${(- 32)}^{\frac{1}{5}}$
(b) ${(243)}^{- \frac{1}{5}}$
(c) $- 125^{\frac{1}{3}}$

Short Answer

Expert verified

Part (a) ${(- 32)}^{\frac{1}{5}} = - 2$

Part (b) ${(243)}^{- \frac{1}{5}} = \frac{1}{3}$

Part (c)role="math" localid="1650608809734" $- 125^{\frac{1}{3}} = - 5$

Step by step solution

Part (a) Step1. Given information

The given expression is ${(- 32)}^{\frac{1}{5}}$ .

Part (a) Step2. Rewrite as a a fifth root .

${(- 32)}^{\frac{1}{5}} = \sqrt[5]{- 32}$

Part (a) Step3. Rewrite -32 as a perfect fifth root

$\sqrt[5]{- 32} = \sqrt[5]{{(- 2)}^{5}}$

Part (a) Step4. Simplification

$\sqrt[5]{{(- 2)}^{5}} = - 2$

Part (b) Step1. Given information

The given expression is ${(243)}^{- \frac{1}{5}}$ .

Part (b) Step2. Rewrite as a fraction with a positive exponent, using the property, a-n=1an .

Write as a fifth root.

${(243)}^{- \frac{1}{5}} = \frac{1}{\sqrt[5]{243}}$

Part (b) Step3. Rewrite 243 as (3)5 .

$\frac{1}{\sqrt[5]{243}} = \frac{1}{\sqrt[5]{{(3)}^{5}}}$

Part (b) Step4. Simplification

$\frac{1}{\sqrt[5]{{(3)}^{5}}} = \frac{1}{3}$

Part (c) Step1. Given information

The given expression is $- 125^{\frac{1}{3}}$ .

Part (b) Step2. The exponent applies only to the 125 .

$- 125^{\frac{1}{3}} = - (125^{\frac{1}{3}})$

Part (c) Step3. Rewrite as a cube root .

$- (125^{\frac{1}{3}}) = - \sqrt[3]{125}$

Part (c) Step4. Rewrite 125 as 53 .

$- \sqrt[3]{125} = - \sqrt[3]{{(5)}^{3}}$

Part (c) Step5. Simplification

$- \sqrt[3]{{(5)}^{3}} = - 5$

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91影视

In the following exercises, simplify.
(a) ${(- 32)}^{\frac{1}{5}}$
(b) ${(243)}^{- \frac{1}{5}}$
(c) $- 125^{\frac{1}{3}}$

Short Answer

Step by step solution

Part (a) Step1. Given information

Part (a) Step2. Rewrite as a a fifth root .

Part (a) Step3. Rewrite -32 as a perfect fifth root

Part (a) Step4. Simplification

Part (b) Step1. Given information

Part (b) Step2. Rewrite as a fraction with a positive exponent, using the property, a-n=1an .

Part (b) Step3. Rewrite 243 as (3)5 .

Part (b) Step4. Simplification

Part (c) Step1. Given information

Part (b) Step2. The exponent applies only to the 125 .

Part (c) Step3. Rewrite as a cube root .

Part (c) Step4. Rewrite 125 as 53 .

Part (c) Step5. Simplification

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91影视

In the following exercises, simplify.(a)(-32)15(b)(243)-15(c)-12513

Short Answer

Step by step solution

Part (a) Step1. Given information

Part (a) Step2. Rewrite as a a fifth root .

Part (a) Step3. Rewrite -32 as a perfect fifth root

Part (a) Step4. Simplification

Part (b) Step1. Given information

Part (b) Step2. Rewrite as a fraction with a positive exponent, using the property, a-n=1an .

Part (b) Step3. Rewrite 243 as (3)5 .

Part (b) Step4. Simplification

Part (c) Step1. Given information

Part (b) Step2. The exponent applies only to the 125 .

Part (c) Step3. Rewrite as a cube root .

Part (c) Step4. Rewrite 125 as 53 .

Part (c) Step5. Simplification

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Study anywhere. Anytime. Across all devices.

In the following exercises, simplify.
(a) ${(- 32)}^{\frac{1}{5}}$
(b) ${(243)}^{- \frac{1}{5}}$
(c) $- 125^{\frac{1}{3}}$