Answer
$\dfrac{y^{\frac{1}{8}}}{x^{\frac{1}{3}}}$
Work Step by Step
Simplify. $(x^{\frac{-2}{3}}y^{\frac{1}{4}} )^\frac{1}{2}$
Since, the power raised to a same exponent or base gets subtract when they are divide and the power raised to a each base gets add.
Thus, $(x^{\frac{-2}{3}}y^{\frac{1}{4}} )^\frac{1}{2}=x^{\frac{-2}{6}}y^{\frac{1}{8}}$
or,$=x^{\frac{-1}{3}}y^{\frac{1}{8}}$
Hence, $=\dfrac{y^{\frac{1}{8}}}{x^{\frac{1}{3}}}$
