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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 460. (page 1124)

Simplify:
(a) $\sqrt[3]{216 a^{6}}$
(b)role="math" localid="1650579633422" $\sqrt[5]{32 b^{20}}$

Short Answer

Expert verified

(a) $\sqrt[3]{216 a^{6}} = 6 a^{2}$

(b) $\sqrt[5]{32 b^{20}} = 2 b^{4}$

Step by step solution

01

Part (a) Step 1: Given Information

The given expression is $\sqrt[3]{216 a^{6}}$ .

02

Part (a) Step 2: Simplification

It can be written as $\sqrt[3]{216 a^{6}} = \sqrt[3]{{(6 a^{2})}^{3}}$

Taking cube root

$= 6 a^{2}$

03

Part (b) Step 1: Given Information

The given expression is $\sqrt[5]{32 b^{20}}$

04

Part (b) Step 2: Simplification

It can be written as $\sqrt[5]{32 b^{20}} = \sqrt[5]{{(2 b^{4})}^{5}}$

Taking fifth root

$= 2 b^{4}$

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