#### Answer

$(\frac{1}{4})^{-2}=16$

#### Work Step by Step

We know that if $b\gt0$ and $b\ne1$, then $y=log_{b}x$ is equivalent to $x=b^{y}$ (where $x\gt0$ and $y$ is a real number).
Therefore, $log_{\frac{1}{4}}16=-2$ can be written as the exponential equation $(\frac{1}{4})^{-2}=16$.