Answer
$x\sqrt[7] {x^2y^{2}}$.
Work Step by Step
The given expression is
$=\frac{\sqrt[7] {x^4y^9}}{\sqrt [7]{x^{-5}y^7}}$
Divide the radicands and retain the common index.
$=\sqrt[7] {\frac{x^4y^9}{x^{-5}y^7}}$
Divide factors in the radicand. Subtract exponents on common bases.
$=\sqrt[7] {x^{4+5}y^{9-7}}$
Simplify.
$=\sqrt[7] {x^{9}y^{2}}$
Factor the radicands as a power of $7$.
$=\sqrt[7] {x^{7}x^2y^{2}}$
Factor into two radicals.
$=\sqrt[7] {x^{7}}\sqrt[7] {x^2y^{2}}$
Simplify.
$=x\sqrt[7] {x^2y^{2}}$.
