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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 9.194 (page 1118)

Simplify: $(a) \sqrt[3]{\frac{m^{13}}{m^{7}}} (b) \sqrt[5]{\frac{n^{12}}{n^{2}}}$

Short Answer

Expert verified

The simplification of the expressions are:

$(a) \sqrt[3]{\frac{m^{13}}{m^{7}}} = m^{2} (b) \sqrt[5]{\frac{n^{12}}{n^{2}}} = n^{2}$

Step by step solution

01

Part (a) Step 1. Given Information

Given expression is $\sqrt[3]{\frac{m^{13}}{m^{7}}}$

02

Part (a) Step 2: Simplification

$\sqrt[3]{\frac{m^{13}}{m^{7}}} = \sqrt[3]{m^{13 - 7}} = \sqrt[3]{m^{6}} = m^{2}$

03

Part (b) Step 1: Given information

Given expression is $\sqrt[5]{\frac{n^{12}}{n^{2}}}$

04

Part (b) Step 2: Simplification

$\sqrt[5]{\frac{n^{12}}{n^{2}}} = \sqrt[5]{n^{12 - 2}} = \sqrt[5]{n^{10}} = n^{2}$

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