Answer
$\sqrt[7]{77x^5y^3}$
Work Step by Step
RECALL:
(i) For nonegative numbers a and b,
$\sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{ab}$
(ii) $a^m \cdot a^n = a^{m+n}$
Use the rules above to obtain:
$=\sqrt[7]{(7x^2y)(11x^3y^2)}
\\=\sqrt[7]{77x^{2+3}y^{1+2}}
\\=\sqrt[7]{77x^5y^3}$