Answer
$$ \lim _{x \rightarrow \infty} \left(\frac{1}{4}\right)^{-x}=\frac{1}{0}=\infty. $$
Work Step by Step
Since $\frac{1}{4}<1$, then we have $$ \lim _{x \rightarrow \infty} \left(\frac{1}{4}\right)^{x}=0. $$
and hence $$ \lim _{x \rightarrow \infty} \left(\frac{1}{4}\right)^{-x}=\frac{1}{0}=\infty. $$
