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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 45 (page 756)

In the following exercises, simplify using absolute values as necessary.
$鈸� \sqrt[3]{216 a^{6}} 鈸� \sqrt[5]{32 b^{20}}$

Short Answer

Expert verified

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

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

Step by step solution

01

Part(a) Step 1. Given information

Simplify using absolute values as necessary.

鈸� \sqrt[3]{216 a^{6}}

02

Step 2. Explanaiton

$\begin{array}{l} Since \\ 鈬� 216 a^{6} = {(6 a^{2})}^{3} \\ 鈬� \sqrt[3]{216 a^{6}} \\ 鈬� \sqrt[3]{{(6 a^{2})}^{3}} \\ 鈬� 6 a^{2} \end{array}$

03

Part(b) Step 1. Given informaiton

$鈸� \sqrt[5]{32 b^{20}}$

Simplify using absolute values as necessary.

04

Step 2. Explanation

$\begin{array}{l} Since \\ 鈬� 32 b^{20} = {(2 b^{4})}^{5} \\ 鈬� \sqrt[5]{32 b^{20}} \\ 鈬� \sqrt[5]{{(2 b^{4})}^{5}} \\ 鈬� 2 b^{4} \end{array}$

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