Answer
$(7xy^2)^{\frac{5}{6}}$
Work Step by Step
RECALL:
$(\sqrt[n]{a})^m=\left(a^{\frac{1}{n}}\right)^m=a^{\frac{m}{n}}$
For the given expression, $n=6$, $a=7xy^2$, and $m=5$.
Thus, using the rule above gives:
$\left(\sqrt[6]{7xy^2}\right)^5=\left((7xy^2)^{\frac{1}{6}}\right)^5=(7xy^2)^{\frac{5}{6}}$
