Q 560. 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 560. (page 1144)

In the following exercises, simplify.
(a) $25^{\frac{3}{2}}$
(b) $9^{- \frac{3}{2}}$
(c) ${(- 64)}^{\frac{2}{3}}$

Short Answer

Expert verified

Part (a) $25^{\frac{3}{2}} = 125$

Part (b) $9^{- \frac{3}{2}} = \frac{1}{27}$

Part (c) localid="1657554515278" ${(- 64)}^{\frac{2}{3}} = 16$

Step by step solution

Part (a) Step1. Given information

The given expression is $25^{\frac{3}{2}}$ .

Part (a) Step2. Rewrite each expression as a radical first using the property, amn=(an)m .

The power of the radical is the numerator of the exponent, $3$ .

Since the denominator of the exponent is $2$ .

role="math" localid="1650715359324" $25^{\frac{3}{2}} = {(\sqrt[2]{25})}^{3}$

Part (a) Step3. Simplification

${(\sqrt[2]{25})}^{3} = {(5)}^{3} = 125$

Part (b) Step1. Given information

The given expression is $9^{- \frac{3}{2}}$ .

Part (b) Step2. Rewrite using b-p=1bp

$9^{- \frac{3}{2}} = \frac{1}{9^{\frac{3}{2}}}$

Part (b) Step3. Change to radical form

$\frac{1}{9^{\frac{3}{2}}} = \frac{1}{{(\sqrt[2]{9})}^{3}}$

Part (b) Step4. Rewrite the radicand as a power

$\frac{1}{{(\sqrt[2]{9})}^{3}} = \frac{1}{{(\sqrt[2]{{(3)}^{2}})}^{3}}$

Part (b) Step5. Simplification

$\frac{1}{{(\sqrt[2]{{(3)}^{2}})}^{3}} = \frac{1}{{(3)}^{3}} = \frac{1}{27}$

Part (c) Step1. Given information

The given expression is ${(- 64)}^{\frac{2}{3}}$ .

Part (c) Step2. Rewrite in radical form

${(- 64)}^{\frac{2}{3}} = {(\sqrt[3]{- 64})}^{2}$

Part (c) Step3. Simplification

${(- 64)}^{\frac{2}{3}} = {(\sqrt[3]{- 64})}^{2} = {(- 4)}^{2} = 16$

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91影视

In the following exercises, simplify.
(a) $25^{\frac{3}{2}}$
(b) $9^{- \frac{3}{2}}$
(c) ${(- 64)}^{\frac{2}{3}}$

Short Answer

Step by step solution

Part (a) Step1. Given information

Part (a) Step2. Rewrite each expression as a radical first using the property, amn=(an)m .

Part (a) Step3. Simplification

Part (b) Step1. Given information

Part (b) Step2. Rewrite using b-p=1bp

Part (b) Step3. Change to radical form

Part (b) Step4. Rewrite the radicand as a power

Part (b) Step5. Simplification

Part (c) Step1. Given information

Part (c) Step2. Rewrite in radical form

Part (c) Step3. Simplification

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91影视

In the following exercises, simplify. (a)2532(b)9-32(c)(-64)23

Short Answer

Step by step solution

Part (a) Step1. Given information

Part (a) Step2. Rewrite each expression as a radical first using the property, amn=(an)m .

Part (a) Step3. Simplification

Part (b) Step1. Given information

Part (b) Step2. Rewrite using b-p=1bp

Part (b) Step3. Change to radical form

Part (b) Step4. Rewrite the radicand as a power

Part (b) Step5. Simplification

Part (c) Step1. Given information

Part (c) Step2. Rewrite in radical form

Part (c) Step3. Simplification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Theoretical and Mathematical Physics

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Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify.
(a) $25^{\frac{3}{2}}$
(b) $9^{- \frac{3}{2}}$
(c) ${(- 64)}^{\frac{2}{3}}$