Answer
$6x^{3}y^{2}$
Work Step by Step
Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the expression above is equivalent to\begin{array}{l}\require{cancel}
\sqrt[3]{12x^2y^5}\sqrt[3]{18x^7y}
\\\\=
\sqrt[3]{12x^2y^5(18x^7y)}
\\\\=
\sqrt[3]{(2\cdot2\cdot3)x^{2+7}y^{5+1}(2\cdot3\cdot3)}
\\\\=
\sqrt[3]{2^33^3x^{9}y^{6}}
.\end{array}
Extracting the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
\sqrt[3]{2^33^3x^{9}y^{6}}
\\\\=
\sqrt[3]{(2\cdot3x^{3}y^{2})^3}
\\\\=
2\cdot3x^{3}y^{2}
\\\\=
6x^{3}y^{2}
.\end{array}
