Answer
$\sqrt[6]{200}$
Work Step by Step
Using $a^{m/n}=\sqrt[n]{a^m}$ and the laws of exponents, then,
\begin{array}{l}
\sqrt[3]{5}\cdot\sqrt[]{2}
\\\\=
5^{\frac{1}{3}}\cdot2^{\frac{1}{2}}
\\\\=
5^{\frac{2}{6}}\cdot2^{\frac{3}{6}}
\\\\=
(5^2\cdot2^3)^{\frac{1}{6}}
\\\\=
(25\cdot8)^{\frac{1}{6}}
\\\\=
(200)^{\frac{1}{6}}
\\\\=
\sqrt[6]{200}
.\end{array}
