how do we solve ((81x^-4)/(16y^4))^-(3/4) ?

There is nothing to solve, but we can simplify it:

$$(\frac{81x^{-4}}{16y^4})^{-\frac{3}{4}}\\\\ (\frac{81}{16x^4y^4})^{-\frac{3}{4}}\\\\ (\frac{81^{\frac{1}{4}}}{16^{\frac{1}{4}}x^{4\frac{1}{4}}y^{4\frac{1}{4}}})^{-3}\\\\ (\frac{3}{2xy})^{-3}\\\\ \frac{2^3x^3y^3}{3^3}\\\\ \frac{8x^3y^3}{27}$$