Answer
$\dfrac{x^{\frac{1}{4}}y^{\frac{1}{4}}}{2}$
Work Step by Step
RECALL:
(i) $\sqrt[n]{a^m} = a^{\frac{m}{n}}$
(ii) $\dfrac{a^m}{a^n}=a^{m-n}, a\ne0$
(iii) $(am)^m = a^mb^m$
Simplify the denominator:
$=\dfrac{\sqrt{xy}}{\sqrt[4]{2^4xy}}
\\=\dfrac{\sqrt{xy}}{2\sqrt[4]{xy}}
\\=\dfrac{1}{2} \cdot \dfrac{\sqrt{xy}}{\sqrt[4]{xy}}$
Use rule (i) above to obtain:
$=\dfrac{1}{2} \cdot \dfrac{(xy)^{\frac{1}{2}}}{(xy)^{\frac{1}{4}}}$
Use rule (ii) above to obtain:
$=\frac{1}{2} \cdot (xy)^{\frac{1}{2} - \frac{1}{4}}
\\=\frac{1}{2} \cdot (xy)^{\frac{2}{4} - \frac{1}{4}}
\\=\frac{1}{2} \cdot (xy)^{\frac{1}{4}}
\\=\dfrac{(xy)^{\frac{1}{4}}}{2}$
Use rule (iii) above to obtain:
$\\=\dfrac{x^{\frac{1}{4}}y^{\frac{1}{4}}}{2}$
