Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$6x^{3}y^{2}$
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}