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 - Page 371: 25

Answer

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

Work Step by Step

Extracting the perfect powers of the index, the given expression, $ \sqrt[3]{-250x^6y^5} ,$ is equivalent to \begin{align*} & \sqrt[3]{-125x^6y^3\cdot2y^2} \\\\&= \sqrt[3]{\left(-5x^2y\right)^3\cdot2y^2} \\\\&= -5x^2y\sqrt[3]{2y^2} .\end{align*} Hence, the simplified form of the given expression is $ -5x^2y\sqrt[3]{2y^2} $.
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