Answer
$\dfrac{\sqrt[4]{9y^6}}{x^2}$
Work Step by Step
RECALL:
The quotient rule:
$\sqrt[n]{\dfrac{a}{b}}=\dfrac{\sqrt[n]{a}}{\sqrt[n]{b}}$
where
$\sqrt[n]{a}$ and $\sqrt[n]{b}$ are real numbers and $b\ne0$
Use the quotient rule above to obtain:
$=\dfrac{\sqrt[4]{9y^6}}{\sqrt[4]{x^{8}}}$
Factor the radicand of the denominator so that at least one factor is a perfect fourth power to obtain:
$=\dfrac{\sqrt[4]{9y^6}}{\sqrt[4]{(x^2)^4}}$
Simplify to obtain;
$=\dfrac{\sqrt[4]{9y^6}}{x^2}$
