Answer
$x=9$
Work Step by Step
Raising both sides to the power of $
\dfrac{2}{3}
$, the solution to the given equation, $
x^{3/2}=27
,$ is
\begin{array}{l}\require{cancel}
\left( x^{\frac{3}{2}} \right)^{\frac{2}{3}}=\left( 3^3 \right)^{\frac{2}{3}}
\\\\
x^{\frac{3}{2}\left(\frac{2}{3}\right)}=3^{3\left(\frac{2}{3}\right)}
\\\\
x^{1}=3^{2}
\\\\
x=9
.\end{array}