Answer
$\dfrac{\sqrt[5]{192x^{6}y^{12}}}{\sqrt[5]{2x^{-1}y^{-3}}}=2xy^{3}\sqrt[5]{3x^{2}}$
Work Step by Step
$\dfrac{\sqrt[5]{192x^{6}y^{12}}}{\sqrt[5]{2x^{-1}y^{-3}}}$
Rewrite this expression as $\sqrt[5]{\dfrac{192x^{6}y^{12}}{2x^{-1}y^{-3}}}$ and evaluate the division inside the root:
$\dfrac{\sqrt[5]{192x^{6}y^{12}}}{\sqrt[5]{2x^{-1}y^{-3}}}=\sqrt[5]{\dfrac{192x^{6}y^{12}}{2x^{-1}y^{-3}}}=\sqrt[5]{96x^{6+1}y^{12+3}}=\sqrt[5]{96x^{7}y^{15}}=...$
Rewrite the expression inside the root as $32\cdot3\cdot x^{7}y^{15}$ and simplify:
$...=\sqrt[5]{32\cdot3\cdot x^{7}y^{15}}=2xy^{3}\sqrt[5]{3x^{2}}$
