Answer
$\frac{1}{7} {x^{2}}{y^{-\frac{3}{2}}}$
Work Step by Step
$(49x^{-2}y^{4})^{-\frac{1}{2}}$ (x$y^{\frac{1}{2}}$)
= $\frac{(xy^{\frac{1}{2}})}{(49x^{-2}y^{4})^{\frac{1}{2}}}$
= $\frac{(xy^{\frac{1}{2}})}{(49^{\frac{1}{2}}x^{-2\times\frac{1}{2}}y^{4\times\frac{1}{2}})}$
= $\frac{(xy^{\frac{1}{2}})}{(\sqrt 49 x^{-1}y^{2})}$
= $\frac{(x^{1+1})}{(7 y^{2-\frac{1}{2}})}$
= $\frac{(x^{2})}{7 (y^{\frac{3}{2}})}$
= $\frac{1}{7}\times\frac{x^{2}}{y^{\frac{3}{2}}}$
=$\frac{1}{7} {x^{2}}{y^{-\frac{3}{2}}}$
