#### Answer

$\dfrac{5\sqrt[8]y}{\sqrt[4]x}$

#### Work Step by Step

Simplify. $(25x^{\frac{-1}{2}}y^{\frac{1}{4}})^{\frac{1}{2}}$
$(25x^{\frac{-1}{2}}y^{\frac{1}{4}})^{\frac{1}{2}}=(25)^{\frac{1}{2}}(x^{\frac{-1}{2}})^{\frac{1}{2}}(y^{\frac{1}{4}})^{\frac{1}{2}}$
or, $=5(x)^{\frac{-1}{4}}y^{\frac{1}{8}}$
Thus, $=5(\dfrac{1}{\sqrt[4]x})(\sqrt[8]y)$
It can be written as $\dfrac{5\sqrt[8]y}{\sqrt[4]x}$