Answer
$-4ab\sqrt[4]{2b}$
Work Step by Step
Using the properties of radicals, the expression $
2a\sqrt[4]{32b^5}-3b\sqrt[4]{162a^4b}+\sqrt[4]{2a^4b^5}
$ simplifies to
\begin{array}{l}
2a\sqrt[4]{16b^4\cdot2b}-3b\sqrt[4]{81a^4\cdot2b}+\sqrt[4]{a^4b^4\cdot2b}
\\=
2a\cdot2b\sqrt[4]{2b}-3b\cdot3a\sqrt[4]{2b}+ab\sqrt[4]{2b}
\\=
4ab\sqrt[4]{2b}-9ab\sqrt[4]{2b}+ab\sqrt[4]{2b}
\\=
-4ab\sqrt[4]{2b}
.\end{array}
