Answer
$8$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
\dfrac{20^{3/2}}{5^{3/2}}
,$ use the laws of exponents.
$\bf{\text{Solution Details:}}$
Using the extended Power Rule of the laws of exponents which states that $\left( \dfrac{x^m}{z^p} \right)^q=\dfrac{x^{mq}}{z^{pq}},$ the expression above is equivalent to\begin{array}{l}\require{cancel}
\left(\dfrac{20}{5}\right)^{3/2}
\\\\=
4^{3/2}
.\end{array}
Using the definition of rational exponents which is given by $a^{\frac{m}{n}}=\sqrt[n]{a^m}=\left(\sqrt[n]{a}\right)^m,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
(\sqrt{4})^{3}
\\\\=
(2)^{3}
\\\\=
8
.\end{array}
