Answer
$\dfrac{1}{64}$
Work Step by Step
Since $16=4^2$, the given expression is equivalent to:
$16^{-\frac{3}{2}}=(4^2)^{-\frac{3}{2}}$
Use the rule $\left(a^m\right)^n=a^{mn}$, then simplify to obtain:
$=4^{2\cdot\frac{-3}{2}}$
$=4^{-3}$
Use the rule $a^{-m}=\dfrac{1}{a^m}$, then simplify to obtain:.
$=\dfrac{1}{4^{3}}$
$=\dfrac{1}{64}$
Hence, the correct answer is $\frac{1}{64}$.
