Answer
$64w^{9/2}x^{3/8}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the laws of exponents to simplify the given expression, $
\left( \dfrac{2^{-2}w^{-3/4}x^{-5/8}}{ w^{3/4}x^{-1/2}} \right)^{-3}
.$
$\bf{\text{Solution Details:}}$
Using the extended Power Rule of the laws of exponents which states that $\left( \dfrac{x^my^n}{z^p} \right)^q=\dfrac{x^{mq}y^{nq}}{z^{pq}},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{2^{-2\cdot(-3)}w^{-\frac{3}{4}\cdot(-3)}x^{-\frac{5}{8}\cdot(-3)}}{ w^{\frac{3}{4}\cdot(-3)}x^{-\frac{1}{2}\cdot(-3)}}
\\\\=
\dfrac{2^{6}w^{\frac{9}{4}}x^{\frac{15}{8}}}{ w^{-\frac{9}{4}}x^{\frac{3}{2}}}
\\\\=
\dfrac{64w^{\frac{9}{4}}x^{\frac{15}{8}}}{ w^{-\frac{9}{4}}x^{\frac{3}{2}}}
.\end{array}
Using the Quotient Rule of the laws of exponents which states that $\dfrac{x^m}{x^n}=x^{m-n},$ the expression above simplifies to
\begin{array}{l}\require{cancel}
64w^{\frac{9}{4}-\left(-\frac{9}{4}\right)}x^{\frac{15}{8}-\frac{3}{2}}
\\\\=
64w^{\frac{9}{4}+\frac{9}{4}}x^{\frac{15}{8}-\frac{3}{2}}
\\\\=
64w^{\frac{18}{4}}x^{\frac{15}{8}-\frac{3}{2}}
\\\\=
64w^{\frac{9}{2}}x^{\frac{15}{8}-\frac{3}{2}}
.\end{array}
Changing the exponent to similar fractions, the expression above is equivalent to
\begin{array}{l}\require{cancel}
64w^{\frac{9}{2}}x^{\frac{15}{8}-\frac{12}{8}}
\\\\=
64w^{\frac{9}{2}}x^{\frac{3}{8}}
\\\\=
64w^{9/2}x^{3/8}
.\end{array}
