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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 9: Q 9.214. (page 1131)

Simplify:
a) ${(- 32)}^{\frac{1}{5}}$
b) $- 32^{\frac{1}{5}}$
c) $32^{\frac{- 1}{5}}$

Short Answer

Expert verified

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

b) $- 32^{\frac{1}{5}} = - 2$

c) $32^{\frac{- 1}{5}} = \frac{1}{2}$

Step by step solution

01

Part (a) Step 1: Given Information

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

02

Part (a) Step 2: Simplification

Rewrite as fifth root.

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

Recognize as perfect fifth power

role="math" localid="1650513107309" $= \sqrt[5]{{(- 2)}^{5}}$

Simplify

$= - 2$

03

Part (b) Step 1: Given Information

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

04

Part (b) Step 2: Simplification

The exponent only applies to $32$ .

Rewrite as fifth power.

role="math" localid="1650513253564" $= - \sqrt[5]{32}$

Recognize as perfect fifth root and simplify

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

$= - 2$

05

Part (c) Step 1: Given Information

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

06

Part (c) Step 2: Simplification

Rewrite as fraction with positive exponent.

$= \frac{1}{\sqrt[5]{32}}$

Recognize as perfect fifth power and simplify

$= \frac{1}{\sqrt[5]{2^{5}}}$

$= \frac{1}{2}$

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