Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.3 - Multiplying and Simplifying Radical Expressions - Concept and Vocabulary Check - Page 530: 5

Answer

$x^5$, $x^4$, and $x^5$.

Work Step by Step

$=\sqrt {x^{10}}$ We can write. $=\sqrt[2] {x^{10}}$ Use $\sqrt [n] x=x^{\frac{1}{n}}$. $=\left ( x^{10} \right )^{\frac{1}{2}}$ Use $(a)^m=a^m$. $=x^{\frac{10}{2}}$ $=x^5$. $=\sqrt[3] {x^{12}}$ Use $\sqrt [n] x=x^{\frac{1}{n}}$. $=\left ( x^{12} \right )^{\frac{1}{3}}$ Use $(a)^m=a^m$. $=x^{\frac{12}{3}}$ $=x^4$. $=\sqrt[6] {x^{30}}$ Use $\sqrt [n] x=x^{\frac{1}{n}}$. $=\left ( x^{30} \right )^{\frac{1}{6}}$ Use $(a)^m=a^m$. $=x^{\frac{30}{6}}$ $=x^5$.
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