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: 27


$-2xy\sqrt[5]{xy^2} $

Work Step by Step

Extracting the perfect powers of the index, the given expression, $ \sqrt[5]{-32x^6y^7} ,$ is equivalent to \begin{align*} & =\sqrt[5]{-32x^5y^5\cdot xy^2} \\\\&= \sqrt[5]{(-2xy)^5\cdot xy^2} \\\\&= -2xy\sqrt[5]{xy^2} .\end{align*} Hence, the simplified form of the given expression is $ -2xy\sqrt[5]{xy^2} $.
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