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 - Test: Chapter 10: 12

Answer

$\sqrt[5]{3x^{4}y}$

Work Step by Step

Using the Quotient Rule of radicals which is given by $\sqrt[n]{\dfrac{x}{y}}=\dfrac{\sqrt[n]{x}}{\sqrt[n]{y}}{},$ the given expression is equivalent to \begin{array}{l}\require{cancel} \dfrac{\sqrt[5]{48x^6y^{10}}}{\sqrt[5]{16x^2y^9}} \\\\= \sqrt[5]{\dfrac{48x^6y^{10}}{16x^2y^9}} \\\\= \sqrt[5]{\dfrac{\cancel{16}(3)x^{6-2}y^{10-9}}{\cancel{16}}} \\\\= \sqrt[5]{3x^{4}y^{1}} \\\\= \sqrt[5]{3x^{4}y} .\end{array}
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