Answer
$x^2y$
Work Step by Step
Use $\dfrac{a^n}{a^m}=a^{n-m}$ to obtain:
$\sqrt[4]{\dfrac{x^9y^7}{xy^3}}=\sqrt[4]{x^{9-1}y^{7-3}}$
Simplify.
$=\sqrt[4]{x^{8}y^{4}}$
Use $x^{8}=(x^2)^4$.
$=\sqrt[4]{(x^2)^4(y^4)}$
Separate using the rule $\sqrt[n]{a\cdot b}=\sqrt[n]{a} \cdot \sqrt[n]{b}, a,b>0$ to obtain:
$=\sqrt[4]{(x^2)^4}\sqrt[4]{y^4}$
Simplify.
$=x^2y$
Hence, the correct answer is $x^2y$.
