Answer
$\sqrt[6]{125r^3s^2}$
Work Step by Step
Using $a^{m/n}=\sqrt[n]{a^m}$ and the laws of exponents, then,
\begin{array}{l}
\sqrt[]{5r}\cdot\sqrt[3]{s}
\\\\=
(5r)^{\frac{1}{2}}\cdot s^{\frac{1}{3}}
\\\\=
(5r)^{\frac{3}{6}}\cdot s^{\frac{2}{6}}
\\\\=
((5r)^3\cdot s^2)^{\frac{1}{6}}
\\\\=
(125r^3\cdot s^2)^{\frac{1}{6}}
\\\\=
(125r^3s^2)^{\frac{1}{6}}
\\\\=
\sqrt[6]{125r^3s^2}
.\end{array}
