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

$8$
Using the laws of exponents, the given expression, $\left( \dfrac{1}{16} \right)^{-3/4} ,$ is equivalent to \begin{array}{l}\require{cancel} 16^{3/4} .\end{array} Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the expression, $16^{3/4} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[4]{16^3} \\\\= \left( \sqrt[4]{16} \right) ^3 \\\\= \left( \sqrt[4]{(2)^4} \right) ^3 \\\\= \left( 2 \right) ^3 \\\\= 8 .\end{array}