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: 40

Answer

$5x\sqrt[3]{x^2y^2}$

Work Step by Step

RECALL: $\dfrac{\sqrt[3]{a}}{\sqrt[3]{b}} = \sqrt[3]{\dfrac{a}{b}}.$ Use the rule above to have $\require{cancel} \sqrt[3]{\dfrac{250x^7y^3}{2x^2y}} \\=\sqrt[3]{\dfrac{\cancel{250}125\cancel{x^7}x^5\cancel{y^3}y^2}{\cancel{2x^2y}}} \\=\sqrt[3]{125x^5y^2} \\=\sqrt[3]{125x^3(x^2y^2)} \\=\sqrt[3]{(5x)^3(x^2y^2)} \\=5x\sqrt[3]{x^2y^2}.$
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