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: 53

Answer

$\dfrac{\sqrt[3]{2xy^2}}{xy}$

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}
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