Answer
The error is in the first step, for $27$ should also be raised to the power 2 under the root.
The correct answer is $9\sqrt[3]{y^{2}}$.
Work Step by Step
The error is in the first step, for $27$ should also be raised to the power 2 under the root.
$\sqrt[n]{a^{m}}=a^{m/n}$
$(27y)^{2/3}= \sqrt[3]{(27y)^{2}}$
$= \sqrt[3]{(3^{3}y)^{2}}$
$= \sqrt[3]{(3^{6})(y^{2})}$
$= \sqrt[3]{(3^{2})^{3}(y^{2})}$
$=3^{2}\sqrt[3]{y^{2}}$
$=9\sqrt[3]{y^{2}}$
