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: 53



Work Step by Step

Multiplying the given expression, $ \sqrt[3]{\dfrac{2}{x^2y}} ,$ by an expression equal to $1$ such that the denominator becomes a perfect power of the index results to \begin{array}{l}\require{cancel} \sqrt[3]{\dfrac{2}{x^2y}} \\\\= \sqrt[3]{\dfrac{2}{x^2y}\cdot\dfrac{xy^2}{xy^2}} \\\\= \sqrt[3]{\dfrac{2xy^2}{x^3y^3}} .\end{array} Using the Quotient Rule of radicals which is given by $\sqrt[n]{\dfrac{x}{y}}=\dfrac{\sqrt[n]{x}}{\sqrt[n]{y}}{},$ the expression above is equivalent to \begin{array}{l}\require{cancel} \sqrt[3]{\dfrac{2xy^2}{x^3y^3}} \\\\= \dfrac{\sqrt[3]{2xy^2}}{\sqrt[3]{x^3y^3}} \\\\= \dfrac{\sqrt[3]{2xy^2}}{\sqrt[3]{(xy)^3}} \\\\= \dfrac{\sqrt[3]{2xy^2}}{xy} .\end{array}
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.