Answer
$3ab\sqrt[4]2b$
Work Step by Step
$\sqrt[4] (162a^{4}b^{5})=\sqrt[4] (81a^{4}b^{4}\times 2b)=\sqrt[4] (81a^{4}b^{4})\times \sqrt[4]2b=3ab\sqrt[4]2b$
We know that $\sqrt[4] (81a^{4}b^{4})=3ab$, because $(3ab)^{4}=3^{4}a^{4}b^{4}=81a^{4}b^{4}$.