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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 463. (page 1124)

Simplify:
(a) $\sqrt[5]{u^{7}}$
(b) $\sqrt[6]{v^{11}}$

Short Answer

Expert verified

(a) $\sqrt[5]{u^{7}} = u \sqrt[5]{u^{2}}$

(b)localid="1650992772336" $\sqrt[6]{v^{11}} = v \sqrt[6]{v^{5}}$

Step by step solution

01

Part (a) Step 1: Given Information

The given expression is $\sqrt[5]{u^{7}}$

02

Part (a) Step 2: Simplification

Rewrite radicand as a product using largest fifth power factor.

$\sqrt[5]{u^{7}} = \sqrt[5]{u^{5} u^{2}}$

Write as product of two radicands

$= \sqrt[5]{u^{5}} \sqrt[5]{u^{2}}$

Simplify

$= u \sqrt[5]{u^{2}}$

03

Part (b) Step 1: Given Information

The given expression is $\sqrt[6]{v^{11}}$

04

Part (b) Step 2: Simplification

Rewrite radicands as product using greatest sixth power factor

$\sqrt[6]{v^{11}} = \sqrt[6]{v^{6} v^{5}}$

Write using product of two radicands

$= v \sqrt[6]{v^{5}}$

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