Answer
$5x^{3}y^{2}$
Work Step by Step
$(125x^{9}y^{6})^{1/3}==\qquad$... apply $(ab)^{n}=a^{n}b^{n}$
$=125^{1/3}(x^{9})^{1/3}(y^{6})^{1/3}=$
... recognize a power of 5.
$=(5^{3})^{1/3}(x^{9})^{1/3}(y^{6})^{1/3}=$
... $a^{1/3}$ is the cube root of a. For odd roots, we don't need absolute values.
... apply $(a^{m})^{n}=a^{mn}$
$=5x^{3}y^{2}$
