Answer
$5x^{2}|y|^{3}$
Work Step by Step
$(25x^{4}y^{6})^{1/2}=\qquad$... apply $(ab)^{n}=a^{n}b^{n}$
$=25^{1/2}\cdot(x^{4})^{1/2}\cdot(y^{6})^{1/2}$
$a^{1/2}=\sqrt{a}$, so we need absolute values, $\sqrt{a^{2}}=|a|$
apply $(a^{m})^{n}=a^{mn}$ with this in mind.
$=5\cdot|x^{2}|\cdot|y^{3}|$
a square is never negative, so we can drop the absolute value for $x^{2}$:
$=5x^{2}|y|^{3}$
