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: 26



Work Step by Step

Extracting the perfect powers of the index, the given expression, $ \sqrt[4]{64x^3y^6} ,$ is equivalent to \begin{align*} & =\sqrt[4]{16y^4\cdot4x^3y^2} \\\\&= \sqrt[4]{\left(2y\right)^4\cdot4x^3y^2} \\\\&= |2y|\sqrt[4]{4x^3y^2} \\\\&= 2|y|\sqrt[4]{4x^3y^2} .\end{align*} Hence, the simplified form of the given expression is $ 2|y|\sqrt[4]{4x^3y^2} $.
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