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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 539 (page 1143)

Simplify
a) $216^{\frac{1}{3}}$
b) $32^{\frac{1}{5}}$
c) $81^{\frac{1}{4}}$

Short Answer

Expert verified

Part (a) $216^{\frac{1}{3}} = 6$

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

Part (c) $81^{\frac{1}{4}} = 3$

Step by step solution

01

Part (a) Step 1:Given information

The given expression is $216^{\frac{1}{3}}$

02

Part (a) Step 2:Simplification

Rewrite as a cube root $\sqrt[3]{216}$

Recognize 216 is a perfect cube. $\sqrt[3]{6^{3}}$

Simplify. 6

03

Part (b) Step 1:Given information

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

04

Part (b) Step 2:Simplification

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

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

Simplify. 2

05

Part (c) Step 1:Given information

The given expression is $81^{\frac{1}{4}}$

06

Part (c) Step 2:Simplification

Rewrite as a fourth root. $\sqrt[4]{81}$

Recognize 81 is a perfect fourth power $\sqrt[4]{3^{4}}$

Simplify 3

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Most popular questions from this chapter

Solve: $\sqrt{3 p + 3} + 3 = 5$ .

In the following exercises, solve.

$\sqrt{4 m + 2} + 2 = 6$ .

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In the following exercises, solve:

$2 \sqrt{5 x + 1} - 8 = 0$ .

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