Answer
$\displaystyle \frac{x^{4}}{y^{4}}$
Work Step by Step
$[\displaystyle \frac{x^{6}y^{-3}}{x^{-2}y^{5}}]^{1/2}$ =......use: $\displaystyle \frac{a^{m}}{a^{n}}=a^{m-n}$
$=[x^{6-(-2)}\cdot y^{-3-5}]^{1/2}$
$=[x^{8}\cdot y^{-8}]^{1/2}$ =......use: $(ab)^{m}=a^{m}b^{m}$
$=(x^{8})^{1/2}(y^{-8})^{1/2}$ =......use: $(a^{m})^{n}=a^{mn}$
$=x^{4}y^{-4}$ =......use: $\displaystyle \frac{1}{a^{n}}=a^{-n}$
$= \displaystyle \frac{x^{4}}{y^{4}}$
