There is nothing to solve, but we can simplify it:
$$(\frac{81x^{-4}}{16y^4})^{-\frac{3}{4}}\\\\
(\frac{81}{16x^4y^4})^{-\frac{3}{4}}\\\\
(\frac{81^{\frac{1}{4}}}{16^{\frac{1}{4}}x^{4\frac{1}{4}}y^{4\frac{1}{4}}})^{-3}\\\\
(\frac{3}{2xy})^{-3}\\\\
\frac{2^3x^3y^3}{3^3}\\\\
\frac{8x^3y^3}{27}$$
There is nothing to solve, but we can simplify it:
$$(\frac{81x^{-4}}{16y^4})^{-\frac{3}{4}}\\\\
(\frac{81}{16x^4y^4})^{-\frac{3}{4}}\\\\
(\frac{81^{\frac{1}{4}}}{16^{\frac{1}{4}}x^{4\frac{1}{4}}y^{4\frac{1}{4}}})^{-3}\\\\
(\frac{3}{2xy})^{-3}\\\\
\frac{2^3x^3y^3}{3^3}\\\\
\frac{8x^3y^3}{27}$$