Answer
$\sqrt[4] (2y)$
Work Step by Step
$\sqrt[8] (4y^{2})=(4y^{2})^{\frac{1}{8}}=(2^{2}y^{2})^{\frac{1}{8}}=2^{\frac{2}{8}}y^{\frac{2}{8}}=2^{\frac{1}{4}}y^{\frac{1}{4}}=\sqrt[4] (2y)$
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