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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 9.183 (page 1115)

Simplify: $(a) \sqrt[3]{27 x^{27}} (b) \sqrt[4]{81 q^{28}}$

Short Answer

Expert verified

The simplification of the expressions are:

Part (a) $3 x^{9}$

Part (b) $3 脳 |q^{7}|$

Step by step solution

01

Part (a) Step 1. Given Information

Given expression is $\sqrt[3]{27 x^{27}}$

02

Part (a) Step 2: Simplification

$\sqrt[3]{27 x^{27}} = \sqrt[3]{27} \sqrt[3]{x^{27}} = \sqrt[3]{3^{3}} x^{9} = 3 x^{9}$

03

Part (b) Step 1: Given information

Given expression is $\sqrt[4]{81 q^{28}}$

04

Part (b) Step 2: Simplification

$\sqrt[4]{81 q^{28}} = \sqrt[4]{81} \sqrt[4]{q^{28}} = \sqrt[4]{3^{4}} 脳 |q^{7}| = 3 脳 |q^{7}|$

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