((-4x^3)(y^4))^-3
--------------------------
(2xy^4)^-4
16x^4y^16
=------------------------
-64x^9y^12
-16y^4
=------------------------
64x^5
-y
=------------------------
4x^5
So the final answer is:
-y^4
-------
4x^5
(Btw if "^" is in front of a number, that means it is an exponent, so when your writing this on paper, just write it as a regular exponent without the "^". I had to do that since I'm on a computer.)
Hopefully this was helpful in some way.