## Intermediate Algebra for College Students (7th Edition)

$2xy^3\sqrt[5]{2xy^2}$
Write $64$ as $2^6$ to obtain: $=\sqrt[5]{2^6x^6y^{17}}$ RECALL: $\sqrt[n]{a^n}=a$ Factor the radicand (expression inside the radical sign) so that at least one factor is a perfect fifth power, and then use the rule above to simplify and obtain: $=\sqrt[5]{(2^5x^5y^{15}) \cdot 2xy^2} \\=\sqrt[5]{2^5x^5(y^3)^5 \cdot 2xy^2} \\=2xy^3\sqrt[5]{2xy^2}$