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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 472 (page 1124)

Use the Product Property to Simplify Expressions with Higher Roots
a) $\sqrt[4]{405 m^{10}}$
b) $\sqrt[5]{160 n^{8}}$

Short Answer

Expert verified

Part (a) $\sqrt[4]{405 m^{10}} = 3 m^{2} \sqrt[4]{5 m^{2}}$

Part (b) $\sqrt[5]{160 n^{8}} = 2 n \sqrt[5]{5 n^{3}}$

Step by step solution

01

Part (a) Step 1:Given information

The given expression is $\sqrt[5]{405 m^{10}}$

02

Part (a) Step 2:Simplification

Rewrite the radicand as a product using

perfect fourth power factors $\sqrt[4]{3^{4} m^{8} . 5 m^{2}}$

Rewrite the radical as the product of two radicals $\sqrt[4]{3^{4} m^{8}} . \sqrt[4]{5 m^{2}}$

Simplify $3 m^{2} \sqrt[4]{5 m^{2}}$

03

Part (b) Step 1:Given information

The given expression is $\sqrt[5]{160 n^{8}}$

04

Part (b) Step 2:Simplification

Rewrite the radicand as a product using

perfect fifth power factors $\sqrt[5]{2^{5} n^{5} . 5 n^{3}}$

Rewrite the radical as the product of two radicals. $\sqrt[5]{2^{5} n^{5}} . \sqrt[5]{5 n^{3}}$

Simplify $2 n \sqrt[5]{5 n^{3}}$

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