Answer
$2y\sqrt[3]{2x}$
Work Step by Step
Using the properties of radicals, then,
\begin{array}{l}
\sqrt[3]{54xy^3}-5\sqrt[3]{2xy^3}+y\sqrt[3]{128x}
\\=
\sqrt[3]{27y^3\cdot2x}-5\sqrt[3]{y^3\cdot2x}+y\sqrt[3]{64\cdot2x}
\\=
3y\sqrt[3]{2x}-5\cdot y\sqrt[3]{2x}+y\cdot4\sqrt[3]{2x}
\\=
3y\sqrt[3]{2x}-5y\sqrt[3]{2x}+4y\sqrt[3]{2x}
\\=
2y\sqrt[3]{2x}
.\end{array}
