## Intermediate Algebra (12th Edition)

Published by Pearson

# Chapter 7 - Section 7.2 - Rational Exponents - 7.2 Exercises: 21

#### Answer

not a real number

#### Work Step by Step

As shown on page 445, we know that $a^{\frac{m}{n}}=\sqrt[n] a^{m}=(\sqrt[n] a)^{m}$. Therefore, $(-144)^{\frac{1}{2}}=\sqrt[2] (-144)^{1}=\sqrt -144=$not a real number. We know this because there is no real number $a$, such that $a^{2}=-144$.

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