Chapter 8: Q. 146 (page 787)

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

Short Answer

Expert verified

(a) The answer is $125$

(b) The answer is $\frac{1}{27}$

Step by step solution

Step 1. Part (a) Simplify the expression 2532

We will use the property

$a^{\frac{m}{n}} = (\sqrt[n]{a})^{m}$ and $a^{\frac{m}{n}} = \sqrt[n]{a^{m}}$

$25^{\frac{3}{2}} = 5^{2 \times \frac{3}{2}} = 5^{3} = 125$

Step 2. Part (b) Simplify the expression 9-32

$9^{\frac{- 3}{2}} = 3^{2 \times \frac{- 3}{2}} = 3^{- 3} = \frac{1}{3^{3}} = \frac{1}{27}$

Step 3. Part (c) Simplify the expression -6423

${(- 64)}^{\frac{2}{3}} = {(- 4)}^{3 \times \frac{2}{3}} = {(- 4)}^{2} = 16$

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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

Step 1. Part (a) Simplify the expression 2532

Step 2. Part (b) Simplify the expression 9-32

Step 3. Part (c) Simplify the expression -6423

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In the following exercises, simplify.(a) 2532(b) 9-32(c)-6423

Short Answer

Step by step solution

Step 1. Part (a) Simplify the expression 2532

Step 2. Part (b) Simplify the expression 9-32

Step 3. Part (c) Simplify the expression -6423

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Applied Mathematics

Decision Maths

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

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