Answer
he second step is wrong and the correct answer is
$\frac{4y\sqrt[3]{ 2}}{5}$.
Work Step by Step
The given expression is
$=\sqrt[3]{\frac{128y^3}{125}}$
Use quotient property of cube roots.
$=\frac{\sqrt[3]{128y^3}}{\sqrt[3]{125}}$
Factor as cube terms.
$=\frac{\sqrt[3]{64y^3\cdot 2}}{\sqrt[3]{125}}$
Use $125=5^3$ and $64=4^3$.
$=\frac{\sqrt[3]{4^3y^3\cdot 2}}{\sqrt[3]{5^3}}$
Simplify.
$=\frac{4y\sqrt[3]{ 2}}{5}$
Hence, the second step is wrong and the correct answer is
$\frac{4y\sqrt[3]{ 2}}{5}$.
