$$(\frac{2a^2}{bc^2})^4 = \frac{(2a^2)^4}{(bc^2)^4} = \frac{2^4 \cdot (a^2)^4}{b^4 \cdot (c^2)^4} = \frac{16a^8}{b^4c^8}$$
Ответ: $$\frac{16a^8}{b^4c^8}$$