$\textbf{Answer:}$
$ \frac{27x}{8}$
$\textbf{Explanation:}$
$ \left [ \frac{16x^{-\frac{5}{6}}}{81 \sqrt{x}} \right]^{-\frac{3}{4}}$
$= \left [ \frac{2^4x^{-\frac{5}{6}}} {3^4 x^{\frac{1}{2}}} \right]^{-\frac{3}{4}}$ representing numbers as their prime factors
$= \frac{2^{4 \cdot \left(-\frac{3}{4} \right)} x^{-\frac{5}{6} \left( -\frac{3}{4}\right)}} {3^{4 \left( -\frac{3}{4} \right)} x^{\frac{1}{2} \left( - \frac{3}{4} \right)}}$ distributing the powers
$ = \frac{2^{-3}x^{\frac{5}{8}}}{3^{-3}x^{-\frac{3}{8}}}$
$ =\frac{3^3 x^{\frac{5}{8}- \left(- \frac{3}{8} \right)}}{2^3}$
$ = \frac{27x}{8}$
