Answer
$2xy^{2} \sqrt[5]( x)^{2}$
Work Step by Step
$\frac{\sqrt[5] 64x^{10}y^{3}}{\sqrt[5] 2x^{3}y^{-7}}$
Using the product and quotient rules for exponents and radicals
$= \sqrt[5] \frac{64x^{10}y^{3}}{2x^{3}y^{-7}}$
$= \sqrt[5](32 x^{10-3}. y^{3-(-7)})$
$= \sqrt[5]32 x^{7}. y^{10}$
$= \sqrt[5](2^{5}. x^{7}. y^{10})$
$=(2^{5}. x^{7}. y^{10})^{\frac{1}{5}} $
$=(2^{5}. x^{5}.x^{2}. y^{10})^{\frac{1}{5}} $
$=2xy^{2} \sqrt[5]( x^{2})$
