#### Answer

$x=4$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
x^{5/2}=32
,$ raise both sides to the power $\dfrac{2}{5}$ to make the exponent of the variable equal to $1.$ Then use the definition of rational exponents and the concepts of radicals to solve for the variable.
$\bf{\text{Solution Details:}}$
Raising both sides of the equation to the power $\dfrac{3}{2},$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
\left( x^{\frac{5}{2}} \right)^{\frac{2}{5}}=(32)^{\frac{2}{5}}
\\\\
x=32^{\frac{2}{5}}
.\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}
x=\left(\sqrt[5]{32}\right)^{2}
\\\\
x=\left(2\right)^{2}
\\\\
x=4
.\end{array}