Answer
$\dfrac{64}{27}$
Work Step by Step
Using $x^{-a}=\dfrac{1}{x^a}$ the given expression, $
\left( \dfrac{3}{4} \right)^{-3}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{1}{\left( \dfrac{3}{4} \right)^{3}}
\\\\=
\dfrac{1}{\left( \dfrac{27}{64} \right)}
\\\\=
1\div\dfrac{27}{64}
\\\\=
1\cdot\dfrac{64}{27}
\\\\=
\dfrac{64}{27}
.\end{array}