Answer
See the explanation below.
Work Step by Step
Since, $p^{\frac{m}{n}}=\sqrt[n] {p^m}$
Here, $n$ signifies the index of the radical $a$ and $m$ signifies the power of the exponent and when we take the reciprocal of the exponent it becomes positive such that :$p^{\frac{-m}{n}}=\frac{1}{p^{\frac{m}{n}}}$
Thus, $9^{\frac{-3}{2}}=\frac{1}{9^{\frac{3}{2}}}$
or, $=\dfrac{1}{3^3}$
or, $=\dfrac{1}{27}$
