Answer
$\dfrac{1}{27}$
Work Step by Step
Since $9=3^2$, the given expression is equivalent to.
$9^{-\frac{3}{2}}=(3^2)^{-\frac{3}{2}}$
Use the rule $\left(a^m\right)^n=a^{mn}$, then simplify to obtain:
$=3^{2\cdot\frac{-3}{2}}$
$=3^{-3}$
Use the rule $a^{-m}=\dfrac{1}{a^m}$, then simplify to obtain:.
$=\dfrac{1}{3^{3}}$
$=\dfrac{1}{27}$
Hence, the correct answer is $\frac{1}{27}$.
