[tex]\displaystyle \\
\frac{4^{-2} \times 16^2}{2^3} = \frac{16^2}{4^{2} \times 2^3} =
\frac{(2^4)^2}{(2^2)^{2} \times 2^3} = \\ \\
= \frac{2^{4\times 2}}{2^{2\times 2} \times 2^3} =
\frac{2^{8}}{2^{4} \times 2^3} = 2^{8-4-3} = 2^{8-7} = 2^1 = \boxed{2}
[/tex]
