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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 9.198 (page 1120)

Simplify: $(a) \sqrt[3]{\frac{40 r^{3}}{s^{6}}} (b) \sqrt[4]{\frac{162 m^{14}}{n^{12}}}$

Short Answer

Expert verified

The simplification of the expressions are:

$(a) \sqrt[3]{\frac{40 r^{3}}{s^{6}}} = \frac{2 \sqrt[3]{5} r}{s^{2}} (b) \sqrt[4]{\frac{162 m^{14}}{n^{12}}} = \frac{3 \sqrt[4]{2 m^{2}} 脳 |m^{3}|}{|n^{3}|}$

Step by step solution

01

Step 1. Part (a) Given the information

Given expression is $\sqrt[3]{\frac{40 r^{3}}{s^{6}}}$

02

Step 2. Simplification

$\sqrt[3]{\frac{40 r^{3}}{s^{6}}} = \frac{\sqrt[3]{40 r^{3}}}{s^{2}} = \frac{2 \sqrt[3]{5} r}{s^{2}}$

03

Step 3. Part (b) Given the information

Given expression is $\sqrt[4]{\frac{162 m^{14}}{n^{12}}}$

04

Step 4. Simplification

$\sqrt[4]{\frac{162 m^{14}}{n^{12}}} = \frac{\sqrt[4]{162 m^{14}}}{|n^{3}|} = \frac{3 \sqrt[4]{2 m^{2}} 脳 |m^{3}|}{|n^{3}|}$

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