#### Answer

$\frac{1}{729}$

#### Work Step by Step

We know that $a^{-\frac{m}{n}}=\frac{1}{a^{\frac{m}{n}}}$, where $a^{\frac{m}{n}}$ is a real number.
Therefore, $81^{-\frac{3}{2}}=\frac{1}{81^{\frac{3}{2}}}$.
We know that $a^{\frac{m}{n}}=\sqrt[n] a^{m}=\sqrt[n] (a)^{m}$, where all indicated roots are real numbers.
Therefore, $\frac{1}{81^{\frac{3}{2}}}=\frac{1}{\sqrt 81^{3}}=\frac{1}{(\sqrt 81)^{3}}=\frac{1}{9^{3}}=\frac{1}{729}$.
$\sqrt 81=9$, because $9^{2}=81$