Answer
$x^3y^6$
Work Step by Step
Use the rule $\left(ab\right)^m=a^mb^m$, then simplify to obtain:
$(x^{4}y^{8})^{\frac{3}{4}}=\left(x^4\right)^{\frac{3}{4}}\left(y^8\right)^{\cdot \frac{3}{4}}$
Use the rule $\left(a^m\right)^n=a^{mn}$, then simplify to obtain:
$=x^{4\cdot\frac{3}{4}}y^{8\cdot\frac{3}{4}}\\
=x^3y^6$
Hence, the correct answer is $x^3y^6$.
