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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 537 (page 1143)

Simplify
a) $625^{\frac{1}{4}}$
b) $243^{\frac{1}{5}}$
c) $32^{\frac{1}{5}}$

Short Answer

Expert verified

Part (a) $625^{\frac{1}{4}} = 5$

Part (b) $243^{\frac{1}{5}} = 3$

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

Step by step solution

01

Part (a) Step 1: Given information

The given expression is $625^{\frac{1}{4}}$

02

Part (a) Step 2:Simplification

Rewrite as a fourth root $\sqrt[4]{625}$

Recognize 625 is a perfect fourth power. localid="1657550757566" $\sqrt[4]{5^{4}}$

Simplify. 5

03

Part (b) Step 1:Given information

The expression is $243^{\frac{1}{5}}$

04

Part (b) Step 2:Simplification

Rewrite as a fifth root $\sqrt[5]{243}$

Recognize 243 is a perfect fifth power $\sqrt[5]{3^{5}}$

Simplify. 3

05

Part (c) Step 1:Given information

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

06

Part (c)Step 2:Simplification

Rewrite as a fifth root $\sqrt[5]{32}$

Recognize 32 is a perfect fifth power. $\sqrt[5]{2^{5}}$

Simplify. 2

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