Answer
$\dfrac{16}{a^{4}}$
Work Step by Step
Using $\left( \dfrac{a}{b} \right)^{x}=\dfrac{a^x}{b^x}
$, the given expression, $
\left( \dfrac{a}{2} \right)^{-4}
$, is equivalent to
\begin{array}{l}
\dfrac{a^{-4}}{2^{-4}}
.\end{array}
Using $a^{-x}=\dfrac{1}{a^{x}}$ and $\dfrac{1}{a^{-x}}=a^x$, the expression above is equivalent to
\begin{array}{l}
\dfrac{2^{4}}{a^{4}}
\\\\=
\dfrac{16}{a^{4}}
.\end{array}