Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - 10.4 Dividing Radical Expressions - 10.4 Exercise Set - Page 653: 26



Work Step by Step

Using the properties of radicals, the given expression, $ \sqrt[5]{\dfrac{243a^9}{b^{13}}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\sqrt[5]{243a^9}}{\sqrt[5]{b^{13}}} \\\\= \dfrac{\sqrt[5]{243a^5\cdot a^4}}{\sqrt[5]{b^{10}\cdot b^3}} \\\\= \dfrac{\sqrt[5]{(3a)^5\cdot a^4}}{\sqrt[5]{(b^{2})^5\cdot b^3}} \\\\= \dfrac{3a\sqrt[5]{a^4}}{b^{2}\sqrt[5]{b^3}} \\\\= \dfrac{3a}{b^2}\sqrt[5]{\dfrac{a^4}{b^3}} \end{array} * Note that it is assumed that all variables represent positive numbers.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

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.