#### Answer

$3xy\sqrt[3]{y^2}$

#### Work Step by Step

Using the properties of radicals, the given expression, $
\dfrac{\sqrt[3]{189x^5y^7}}{\sqrt[3]{7x^2y^2}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[3]{\dfrac{189x^5y^7}{7x^2y^2}}
\\\\=
\sqrt[3]{27x^{5-2}y^{7-2}}
\\\\=
\sqrt[3]{27x^{3}y^{5}}
\\\\=
\sqrt[3]{27x^{3}y^{3}\cdot y^2}
\\\\=
\sqrt[3]{(3x^{}y^{})^3\cdot y^2}
\\\\=
3xy\sqrt[3]{y^2}
.\end{array}
* Note that it is assumed that all variables represent positive numbers.