Answer
$\frac{1}{512}$
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, $64^{-\frac{3}{2}}=\frac{1}{64^{\frac{3}{2}}}$.
We know that $a^{\frac{m}{n}}=\sqrt[n] a^{m}=\sqrt[n] (a)^{m}$, where all indicated roots are real numbers.
Therefore, $\frac{1}{64^{\frac{3}{2}}}=\frac{1}{\sqrt 64^{3}}=\frac{1}{(\sqrt 64)^{3}}=\frac{1}{8^{3}}=\frac{1}{512}$.
$\sqrt 64=8$, because $8^{2}=64$
