Q 562. 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 562. (page 1144)

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

Short Answer

Expert verified

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

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

Part (c) ${(- 9)}^{\frac{3}{2}} =$ Not a real number

Step by step solution

Part (a) Step1. Given information

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

Part (a) Step2. Rewrite in radical form

$- 9^{\frac{3}{2}} = - {(\sqrt{9})}^{3}$

Part (a) Step3. Simplify the radical

$- {(\sqrt{9})}^{3} = - {(3)}^{3}$

Part (a) Step4. Simplification

$- {(3)}^{3} = - 27$

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. Rewrite in radical form

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

Part (b) Step4. Simplify the radical

$- (\frac{1}{{(\sqrt{9})}^{3}}) = - (\frac{1}{{(3)}^{3}})$

Part (b) Step5. Simplification

$- (\frac{1}{{(3)}^{3}}) = - \frac{1}{27}$

Part (c) Step1. Given information

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

Part (c) Step2. Rewrite in radical form

${(- 9)}^{\frac{3}{2}} = {(\sqrt{- 9})}^{3}$

Part (c) Step3. Simplification

There is no real number whose cube root is $9$ .

${(- 9)}^{\frac{3}{2}}$

Not a real number.

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91影视

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

Short Answer

Step by step solution

Part (a) Step1. Given information

Part (a) Step2. Rewrite in radical form

Part (a) Step3. Simplify the radical

Part (a) Step4. Simplification

Part (b) Step1. Given information

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

Part (b) Step3. Rewrite in radical form

Part (b) Step4. Simplify the radical

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)-932(b)-9-32(c)(-9)32

Short Answer

Step by step solution

Part (a) Step1. Given information

Part (a) Step2. Rewrite in radical form

Part (a) Step3. Simplify the radical

Part (a) Step4. Simplification

Part (b) Step1. Given information

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

Part (b) Step3. Rewrite in radical form

Part (b) Step4. Simplify the radical

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.

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