Answer
$x^{}y^{}\sqrt[6]{xy^5 }$
Work Step by Step
Using $\sqrt[n]{x^m}=(\sqrt[n]{x})^m=x^{m/n}$, the given expression, $
\sqrt[]{xy^3}\sqrt[3]{x^2y}
,$ is equivalent to
\begin{array}{l}\require{cancel}
(xy^3)^{\frac{1}{2}}\cdot (x^2y)^{\frac{1}{3}}
.\end{array}
Using the laws of exponents, the expression above simplifies to
\begin{array}{l}\require{cancel}
(xy^3)^{\frac{3}{6}}\cdot (x^2y)^{\frac{2}{6}}
\\\\=
\left[(xy^3)^{3}\cdot (x^2y)^{2} \right]^{\frac{1}{6}}
\\\\=
\sqrt[6]{(xy^3)^{3}\cdot (x^2y)^{2} }
\\\\=
\sqrt[6]{(x^3y^9)\cdot (x^4y^2) }
\\\\=
\sqrt[6]{x^{3+4}y^{9+2} }
\\\\=
\sqrt[6]{x^{7}y^{11} }
\\\\=
\sqrt[6]{x^{6}y^{6}\cdot xy^5 }
\\\\=
\sqrt[6]{(x^{}y^{})^6\cdot xy^5 }
\\\\=
x^{}y^{}\sqrt[6]{xy^5 }
.\end{array}
* Note that it is assumed that all variables represent positive numbers.
