#### Answer

$-\frac{3}{4}$

#### 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, $\sqrt[3] \frac{-27}{64}=\frac{\sqrt[3] (-27)}{\sqrt[3] 64}=\frac{-3}{4}=-\frac{3}{4}$.
$\sqrt[3] -27=-3$, because $(-3)^{3}=-27$
$\sqrt[3] 64=4$, because $4^{3}=64$