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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 775 (page 1154)

In the following exercises, simplify
$(a) \sqrt[4]{81 x^{12}} (b) \sqrt[6]{64 y^{18}}$

Short Answer

Expert verified

The simplification of the given expressions are:

$(a) \sqrt[4]{81 x^{12}} = 3 x^{3} (b) \sqrt[6]{64 y^{18}} = 2 y^{3}$

Step by step solution

01

Part (a) Step 1. Given Information

Given expression is $\sqrt[4]{81 x^{12}}$

02

Part (a) Step 2: Simplification

$\sqrt[4]{81 x^{12}} = \sqrt[4]{81} \sqrt[4]{x^{12}} = {(3^{4})}^{\frac{1}{4}} {(x^{12})}^{\frac{1}{4}} = 3 x^{3}$

03

Part (b) Step 1: Given information

Given expression is $\sqrt[6]{64 y^{18}}$

04

Part (b) Step 2: Simplification

$\sqrt[6]{64 y^{18}} = \sqrt[6]{64} \sqrt[6]{y^{18}} = {(2^{6})}^{\frac{1}{6}} {(y^{18})}^{\frac{1}{6}} = 2 y^{3}$

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