## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$\dfrac{16}{a^{4}}$
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}