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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 9.195 (page 1119)

Simplify: $(a) \frac{\sqrt[3]{- 532}}{\sqrt[3]{2}} (b) \frac{\sqrt[4]{486 m^{11}}}{\sqrt[4]{3 m^{5}}}$

Short Answer

Expert verified

The simplification of the expressions are:

$(a) \frac{\sqrt[3]{- 532}}{\sqrt[3]{2}} = - \sqrt[3]{266} (b) \frac{\sqrt[4]{486 m^{11}}}{\sqrt[4]{3 m^{5}}} = 3 \sqrt[4]{2 m^{2}} 脳 |m|$

Step by step solution

01

Part (a) Step 1. Given Information

Given expression is $\frac{\sqrt[3]{- 532}}{\sqrt[3]{2}}$

02

Part (a) Step 2: Simplification

$\frac{\sqrt[3]{- 532}}{\sqrt[3]{2}} = \frac{- \sqrt[3]{532}}{\sqrt[3]{2}} = \frac{- \sqrt[3]{2} 脳 \sqrt[3]{266}}{\sqrt[3]{2}} = - \sqrt[3]{266}$

03

Part (b) Step 1: Given information

Given expression is $\frac{\sqrt[4]{486 m^{11}}}{\sqrt[4]{3 m^{5}}}$

04

Part (b) Step 2: Simplification

$\frac{\sqrt[4]{486 m^{11}}}{\sqrt[4]{3 m^{5}}} = \frac{\sqrt[4]{3 m^{5}} 脳 \sqrt[4]{162 m^{6}}}{\sqrt[4]{3 m^{5}}} = \sqrt[4]{162 m^{6}} = \sqrt[4]{3^{4} 脳 2 m^{4} 脳 m^{2}} = 3 脳 |m| 脳 \sqrt[4]{2 m^{2}} = 3 \sqrt[4]{2 m^{2}} 脳 |m|$

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Most popular questions from this chapter

In the following exercises, simplify.

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In the following exercises, simplify by rationalizing the denominator

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