[tex]\displaystyle\\
2^{-1}+ 4^{-2} = \\\\
= \frac{1}{2^1} + \frac{1}{4^2} =\\\\=\frac{1}{2} + \frac{1}{16} =\\\\
= \frac{1\times 8}{2\times 8} + \frac{1}{16} =\\\\
= \frac{8}{16} + \frac{1}{16} =\frac{8+1}{16} = \boxed{\frac{9}{16}} =\boxed{\frac{3^2}{2^4}}
[/tex]
