Answer
$\frac{5}{16}$
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, $4^{-1}+4^{-2}=\frac{1}{4}+\frac{1}{4^{2}}=\frac{1}{4}+\frac{1}{16}=\frac{1\times4}{4\times4}+\frac{1}{16}=\frac{4}{16}+\frac{1}{16}=\frac{4+1}{16}=\frac{5}{16}$.