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: 50

Answer

$\dfrac{\sqrt[3]{63xy^2}}{3y}$

Work Step by Step

Rationalizing the denominator of the given expression, $ \dfrac{\sqrt[3]{7x}}{\sqrt[3]{3y}} ,$ we find: \begin{array}{l}\require{cancel} \dfrac{\sqrt[3]{7x}}{\sqrt[3]{3y}}\cdot\dfrac{\sqrt[3]{9y^2}}{\sqrt[3]{9y^2}} \\\\= \dfrac{\sqrt[3]{63xy^2}}{\sqrt[3]{27y^3}} \\\\= \dfrac{\sqrt[3]{63xy^2}}{\sqrt[3]{(3y)^3}} \\\\= \dfrac{\sqrt[3]{63xy^2}}{3y} .\end{array} * Note that it is assumed that all variables represent positive numbers.
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