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 7.1 - Radical Expressions and Functions - Concept and Vocabulary Check - Page 511: 11


If n is even: $|a|$; If n is odd: $a$

Work Step by Step

If $n$ is even, then the value of $\sqrt[n]{a^n}$ cannot be negative. Thus, if $n$ is even, $\sqrt[n]{a^n} = |a|$. However, if $n$ is odd, $\sqrt[n]{a^n}$ can be any number. Thus,if $n$ is odd, $\sqrt[n]{a^n} = a$.
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