Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Section 7.3 - Simplifying Radical Expressions - Exercise Set - Page 433: 76



Work Step by Step

Using the properties of radicals, then, \begin{array}{l} \dfrac{\sqrt[5]{192x^{6}y^{12}}}{\sqrt[5]{2x^{-1}y^{-3}}} \\\\= \sqrt[5]{\dfrac{192x^{6}y^{12}}{2x^{-1}y^{-3}}} \\\\= \sqrt[5]{96x^{6-(-1)}y^{12-(-3)}} \\\\= \sqrt[5]{96x^{7}y^{15}} \\\\= \sqrt[5]{32x^5y^{15}\cdot3x^{2}} \\\\= 2xy^3\sqrt[5]{3x^{2}} .\end{array}
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