Whoa, a question rendered in LaTeX. Give the asker a prize.
We're not actually asked anything; let's assume we're to simplify.
[tex]\dfrac{ \sqrt[3]{81 m^4} }{\sqrt[3]{25 x^2 y}}[/tex]
[tex]=\dfrac{ \sqrt[3]{3^4 m^4 }}{\sqrt[3]{25 x^2 y}}[/tex]
[tex]= 3m \sqrt[3]{\dfrac{3m}{25 x^2 y}}[/tex]
I don't think there's any more simplification to do.