#### Answer

$-\frac{6}{5}$

#### Work Step by Step

The quotient rule for radicals tells us that $\sqrt[n] \frac{a}{b}=\frac{\sqrt[n] a}{\sqrt[n] b}$ (if $\sqrt[n] a$ and $\sqrt[n] b$ are real numbers and $n$ is a natural number). That is, the nth root of a quotient is the quotient of the nth roots.
Therefore, $\sqrt[3] \frac{-216}{125}=\frac{\sqrt[3] (-216)}{\sqrt[3] 125}=\frac{-6}{5}=-\frac{6}{5}$.
$\sqrt[3] -216=-6$, because $(-6)^{3}=-216$
$\sqrt[3] 125=5$, because $5^{3}=125$