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 - Test - Page 578: 5


$\sqrt[20] {x^9}$

Work Step by Step

Simplify. $\sqrt[4]{x}\sqrt[5]{x}$ As per definition of square root property,we have $(p)^{\frac{m}{n}}=\sqrt[n] {p^m}$ Therefore, $\sqrt[4]{x}\sqrt[5]{x}=(x)^{\frac{1}{4}}(x)^{\frac{1}{5}}=(x)^{\frac{1}{4}+\frac{1}{5}}=(x)^{\frac{9}{20}}$ Thus, the given radical term can be written as:$\sqrt[20] {x^9}$
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