Answer
$y\sqrt{xy}$
Work Step by Step
RECALL:
(i) $\sqrt[n]{a} = a^{\frac{1}{n}}$
(ii) $\sqrt[n]{a^m} = a^{\frac{m}{n}}$
(iii) $(ab)^m = a^mb^m$
(iv) $(a^m)^n=a^{mn}$
The expression inside the radical sign can be written as:
$=\sqrt[4]{x^2(y^3)^2}
\\=\sqrt[4]{(xy^3)^2}$
Use the rules above to have:
$=\left((xy^3)^2\right)^{\frac{1}{4}}
\\=(xy^3)^{2\cdot\frac{1}{4}}
\\=(xy^3)^{\frac{1}{2}}
\\=\sqrt{xy^3}
\\=\sqrt{x\cdot y^2 \cdot y}
\\=y\sqrt{xy}$
