Chapter 8: Q. 145 (page 787)

In the following exercises, simplify.
(a) $64^{\frac{5}{2}}$
(b) $81^{\frac{- 3}{2}}$
(c) ${(- 27)}^{\frac{2}{3}}$

Short Answer

Expert verified

(a) The answer is $32, 768$

(b) The answer is $\frac{1}{729}$

Step by step solution

Step 1. Part (a) Simplify the expression 6452

We will use the property

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

$64^{\frac{5}{2}} = {(8)}^{2 \times \frac{5}{2}} = 8^{5} = 32, 768$

Step 2. Part (b) Simplify the expression 81-32

${(81)}^{\frac{- 3}{2}} = 9^{2 \times \frac{- 3}{2}} = 9^{- 3} = \frac{1}{9^{3}} = \frac{1}{729}$

Step 3. Part (c) Simplify the expression -2723

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

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In the following exercises, simplify.
(a) $64^{\frac{5}{2}}$
(b) $81^{\frac{- 3}{2}}$
(c) ${(- 27)}^{\frac{2}{3}}$

Short Answer

Step by step solution

Step 1. Part (a) Simplify the expression 6452

Step 2. Part (b) Simplify the expression 81-32

Step 3. Part (c) Simplify the expression -2723

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In the following exercises, simplify.(a) 6452(b) 81-32(c)-2723

Short Answer

Step by step solution

Step 1. Part (a) Simplify the expression 6452

Step 2. Part (b) Simplify the expression 81-32

Step 3. Part (c) Simplify the expression -2723

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Pure Maths

Calculus

Discrete Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify.
(a) $64^{\frac{5}{2}}$
(b) $81^{\frac{- 3}{2}}$
(c) ${(- 27)}^{\frac{2}{3}}$