## Intermediate Algebra (12th Edition)

Published by Pearson

# Chapter 7 - Section 7.3 - Simplifying Radicals, the Distance Formula, and Circles - 7.3 Exercises: 85

#### Answer

$-10r^{5}\sqrt[]{5r}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given expression, $-\sqrt[]{500r^{11}} ,$ find a factor of the radicand that is a perfect power of the index. Then extract the root of that factor. Note that all variables are assumed to represent positive real numbers. $\bf{\text{Solution Details:}}$ Expressing the radicand of the expression above with a factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} -\sqrt[]{100r^{10}\cdot5r} \\\\= -\sqrt[]{(10r^{5})^2\cdot5r} \\\\= -10r^{5}\sqrt[]{5r} .\end{array}

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.