# Chapter 7 - Section 7.2 - Rational Exponents - Exercise Set: 22

negative

#### Work Step by Step

We know that $a^{\frac{m}{n}}=(\sqrt[n] a)^{m}$ (where m and n are positive integers greater than 1 with $\frac{m}{n}$ in simplest form and $\sqrt[n] a$ is a real number). Therefore, $(-9)^{\frac{3}{2}}=(\sqrt -9)^{3}$. However, $\sqrt -9$ is not a real number, as we cannot find some number $b$ such that $b^{2}=-9$. In general, we cannot perform a radical function of a negative number when the index of the radical is even.

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