Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 6 - Radical Functions and Rational Exponents - 6-2 Multiplying and Dividing Radical Expressions - Practice and Problem-Solving Exercises: 41

Answer

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

Work Step by Step

RECALL: $\dfrac{\sqrt[3]{a}}{\sqrt[3]{b}} = \sqrt[3]{\dfrac{a}{b}}.$ Use the rule above to have $\require{cancel} \sqrt[3]{\dfrac{48x^3y^2}{6x^4y}} \\=\sqrt[3]{\dfrac{\cancel{48}8\cancel{x^3}x^2\cancel{y^2}y}{\cancel{6}\cancel{x^4}x^3\cancel{y}}} \\=\sqrt[3]{\dfrac{8x^2y}{x^3}} \\=\sqrt[3]{\dfrac{2^3x^2y}{x^3}} \\=\dfrac{2}{x} \cdot \sqrt[3]{x^2y} \\=\dfrac{2\sqrt[3]{x^2y}}{x}.$
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