$$\left(2a^{2}\right)^{-4}$$
Expand $\left(2a^{2}\right)^{-4}$.$$2^{-4}\left(a^{2}\right)^{-4}$$
To raise a power to another power, multiply the exponents. Multiply $2$ and $-4$ to get $-8$.$$2^{-4}a^{-8}$$
Calculate $2$ to the power of $-4$ and get $\frac{1}{16}$.$$\frac{1}{16}a^{-8}$$