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 - 6-3 Binomial Radical Expressions - Practice and Problem-Solving Exercises - Page 380: 78



Work Step by Step

Using $\sqrt[n]{x}\cdot\sqrt[n]{y}=\sqrt[n]{xy},$ the given expression is equivalent to: \begin{align*} & =\sqrt[3]{2x^2(4x)} \\&= \sqrt[3]{8x^3} \end{align*} Extracting the root of the factors that is a perfect power of the index, the expression above is equivalent to \begin{align*} & =\sqrt[3]{(2x)^3} \\&= 2x \end{align*} Hence, the simplified form of the given expression is $ 2x $.
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