Answer
$\dfrac{1000}{1331}$
Work Step by Step
Using $a^{-x}=\dfrac{1}{a^x}$ or $\dfrac{1}{a^{-x}}=a^x$, the given expression, $
\left( \dfrac{121}{100} \right)^{-3/2}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{1}{\left( \dfrac{121}{100} \right)^{3/2}}
\\\\=
\left( \dfrac{100}{121} \right)^{3/2}
.\end{array}
Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the expression, $
\left( \dfrac{100}{121} \right)^{3/2}
$, simplifies to
\begin{array}{l}\require{cancel}
\left(\sqrt[]{\dfrac{100}{121}} \right)^3
\\\\=
\left(\sqrt[]{\left( \dfrac{10}{11} \right)^2} \right)^3
\\\\=
\left( \dfrac{10}{11} \right)^3
\\\\=
\dfrac{1000}{1331}
.\end{array}
