## Algebra 2 Common Core

$-2xy\sqrt[5]{xy^2}$
Extracting the perfect powers of the index, the given expression, $\sqrt[5]{-32x^6y^7} ,$ is equivalent to \begin{align*} & =\sqrt[5]{-32x^5y^5\cdot xy^2} \\\\&= \sqrt[5]{(-2xy)^5\cdot xy^2} \\\\&= -2xy\sqrt[5]{xy^2} .\end{align*} Hence, the simplified form of the given expression is $-2xy\sqrt[5]{xy^2}$.
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