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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 473 (page 1124)

Use the Product Property to Simplify Expressions with Higher Roots
a) $\sqrt[3]{512 p^{5}}$
b) $\sqrt[4]{324 q^{7}}$

Short Answer

Expert verified

Part (a) $\sqrt[3]{512 p^{5}} = 8 p \sqrt[3]{p^{2}}$

Part (b) $\sqrt[4]{324 q^{7}} = 3 q \sqrt[4]{4 q^{3}}$

Step by step solution

01

Part (a)Step 1:Given information

The given expression is $\sqrt[3]{512 p^{5}}$

02

Part (a)Step 2:Simplification

Rewrite the radicand as a product

using perfect cube factors. $\sqrt[3]{8^{3} q^{3} . q^{2}}$

Rewrite the radical as the product of two radicals $\sqrt[3]{8^{3} q^{3}} . \sqrt[3]{q^{2}}$

Simplify $8 q \sqrt[3]{q^{2}}$

03

Part (b) Step 1:Given information

The given expression is $\sqrt[4]{324 q^{7}}$

04

Part (b)Step 2:Simplification

Rewrite the radicand as a product using

perfect fourth power factors. $\sqrt[4]{3^{4} . 4 . q^{4} . q^{3}}$

Rewrite the radical as the product of two radicals $\sqrt[4]{3^{4} . q^{4}} . \sqrt[4]{4 . q^{3}}$

Simplify $3 q \sqrt[4]{4 q^{3}}$

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