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