Answer
$\sqrt[6] {32}$.
Work Step by Step
The given function is
$=\sqrt{2}\cdot \sqrt[3] 2$
Rewrite as an exponential expression.
$=(2)^{\frac{1}{2}}\cdot (2)^{\frac{1}{3}}$
Use power rule.
$=(2)^{\frac{1}{2}+\frac{1}{3}}$
Simplify.
$=(2)^{\frac{3}{6}+\frac{2}{6}}$
$=(2)^{\frac{3+2}{6}}$
$=(2)^{\frac{5}{6}}$
Rewrite in radical notation.
$=\sqrt[6] {2^5}$
Simplify.
$=\sqrt[6] {32}$.
