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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 482 (page 1125)

Use the Quotient Property to Simplify Expressions with Higher Roots
a) $\frac{\sqrt[4]{64}}{\sqrt[4]{2}}$
b) $\frac{\sqrt[5]{128 x^{8}}}{\sqrt[5]{2 x^{2}}}$

Short Answer

Expert verified

Part (a) $\frac{\sqrt[4]{64}}{\sqrt[4]{2}} = 2 \sqrt[4]{2}$

Part (b) $\frac{\sqrt[5]{128 x^{8}}}{\sqrt[5]{2 x^{2}}} = 2 x \sqrt[5]{2 x}$

Step by step solution

01

Part (a)Step 1:Given informaion

The given expression is $\frac{\sqrt[4]{64}}{\sqrt[4]{2}}$

02

Part (a)Step 2:Simplification

Simplify the fraction under the radical first. $\sqrt[4]{\frac{64}{2}}$

$= \sqrt[4]{32}$

Rewrite the radicand using perfect fourth power factors $\sqrt[4]{2^{4} . 2}$

Simplify $2 \sqrt[4]{2}$

03

Part (b)Step 1:Given information

The given expression is $\frac{\sqrt[5]{128 x^{8}}}{\sqrt[5]{2 x^{3}}}$

04

Part (b)Step 2:Simplification

Simplify the fraction under the radical first. $\sqrt[5]{\frac{128 x^{8}}{2 x^{2}}}$

$= \sqrt[5]{64 x^{6}}$

Rewrite the radicand using perfect fifth power factors $\sqrt[5]{{(2 x)}^{5} . 2 x}$

Simplify $2 x \sqrt[5]{2 x}$

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