Answer
$$\frac{81x^{36}}{256y^8}$$
Work Step by Step
We know the following rules of exponents.
$$ (1) \ a^m\cdot a^n = a^{m+n} \\ (2) \ (ab)^m =a^mb^m \\ (3) \ (a^m)^n =a^{mn} \\ (4)
\ a^{-m} = \frac{1}{a^m} \\ (5)\ \frac{a^m}{a^n} =a^{m-n} \\ (6) \ a^0=1 \\ (7) \ (\frac{a}{b})^m =\frac{a^m}{b^m}$$
Thus, we find:
$$ \left(\frac{3x^4y^{-2}}{4x^{-5}}\right)^4\\ \frac{3^4x^{36}y^{-8}}{4^4}\\ \frac{\frac{81x^{36}}{y^8}}{4^4}\\ \frac{81x^{36}}{256y^8}$$