Answer
$-\frac{1}{2}$
Work Step by Step
We know that $\sqrt[6] \frac{1}{64}=\frac{1}{2}$, because $(\frac{1}{2})^{6}=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{64}$.
Therefore, $-\sqrt[6] \frac{1}{64}=-(\frac{1}{2})=-\frac{1}{2}$.