## Intermediate Algebra (6th Edition)

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, $(-16)^{\frac{3}{4}}=(\sqrt[4] -16)^{3}$. However, $\sqrt[4] -16$ is not a real number, as we cannot find some number $b$ such that $b^{4}=-16$. In general, we cannot perform a radical function of a negative number when the index of the radical is even.