Answer
$\dfrac{x^{2}}{7y^{\frac{3}{2}}}$
Work Step by Step
Simplify. $(49x^{-2}y^4)^{-1/2}(xy^{1/2})$
or, $=(49)^{-1/2}(x^{-2})^{-1/2}(y^4)^{-1/2}(xy^{1/2})$
or, $=\dfrac{x^{1+1} y^{-2+\frac{1}{2}}}{(49)^{1/2}}$
or, $=\dfrac{x^{2} y^{\frac{-3}{2}}}{(7^2)^{1/2}}$
or, $=\dfrac{x^{2}}{7y^{\frac{3}{2}}}$
