[tex]\bf \sqrt[4]{\cfrac{24x^6y}{128x^4y^5}}\implies \cfrac{\sqrt[4]{4x^6y}}{\sqrt[4]{128x^4y^5}}\quad
\begin{cases}
24=2\cdot 2\cdot 2\cdot 3\\
128=2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\\
x^6=x^{4+2}\\
\qquad x^4x^2\\
y^5=y^{4+1}\\
\qquad y^4y^1
\end{cases}[/tex]
[tex]\bf \cfrac{\sqrt[4]{\underline{2\cdot 2\cdot 2}\cdot 3\cdot \underline{x^4} x^2\underline{y}}}{\sqrt[4]{\underline{2\cdot 2\cdot 2}\cdot 2\cdot 2\cdot 2\cdot 2\cdot \underline{x^4} y^4\underline{y^1}}}
\implies
\cfrac{\sqrt[4]{3x^2}}{\sqrt[4]{2^4y^4}}\implies \cfrac{\sqrt[4]{3x^2}}{2y}[/tex]
