Answer
-64
Work Step by Step
We know that $a^{−n}=\frac{1}{a^{n}}$ and $\frac{1}{a^{-n}}=a^{n}$ (as long as a is a nonzero real number and n is an integer).
Therefore, $(-\frac{1}{4})^{-3}=\frac{(-1)^{-3}}{4^{-3}}=\frac{1}{(-1)^{3}}\times4^{3}=\frac{1}{-1}\times64=-1\times64=-64$.