Answer
$3b\sqrt[3]{2a}$
Work Step by Step
Using the properties of radicals, the given expression, $
\sqrt[3]{128ab^3}-3\sqrt[3]{2ab^3}+b\sqrt[3]{16a}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[3]{64b^3\cdot2a}-3\sqrt[3]{b^3\cdot2a}+b\sqrt[3]{8\cdot2a}
\\\\=
\sqrt[3]{(4b)^3\cdot2a}-3\sqrt[3]{(b)^3\cdot2a}+b\sqrt[3]{(2)^3\cdot2a}
\\\\=
4b\sqrt[3]{2a}-3b\sqrt[3]{2a}+2b\sqrt[3]{2a}
\\\\=
3b\sqrt[3]{2a}
.\end{array}
