Chapter 8 - Rational Functions - 8-1 Inverse Variation - Practice and Problem-Solving Exercises - Page 505: 47

$\text{F}$

Recall: $\sqrt[n]{a}=a^{\frac{1}{n}}$ Thus, \begin{align*} \sqrt[6]{81x^4y^8}&=\left(81x^4y^8\right)^{\frac{1}{6}}\\ &=\left(3^4x^4\cdot (y^2)^4\right)^{\frac{1}{6}}\\ &=\left[\left(3xy^2\right)^4\right]^{\frac{1}{6}}\\ &=\left(3xy^2\right)^{\frac{4}{6}}\\ &=\left(3xy^2\right)^{\frac{2}{3}}\\ \end{align*} Thus, the answer is Option F.