Answer
$-\frac{1}{2}$
Work Step by Step
We know that $\sqrt[5] \frac{1}{32}=\frac{1}{2}$, because $(\frac{1}{2})^{5}=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{32}$.
Therefore, $-\sqrt[5] \frac{1}{32}=-(\frac{1}{2})=-\frac{1}{2}$.