Answer
$9$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the laws of exponents to simplify the given expression, $
3^{1/2}\cdot3^{3/2}
.$
$\bf{\text{Solution Details:}}$
Using the Product Rule of the laws of exponents which is given by $x^m\cdot x^n=x^{m+n},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
3^{\frac{1}{2}+\frac{3}{2}}
\\\\=
3^{\frac{4}{2}}
\\\\=
3^{2}
\\\\=
9
.\end{array}
