I asking this question here to just check the work and that I have simplified it correctly.
Given the formula $\Large \sqrt[3]{\frac{12m^4n^8}{5p^4}}$ We need to rationalize the denominator by multiplying by $\Large \sqrt[3]{\frac{25p^4}{25p^4}}$
Doing so would leave $\Large \frac{\sqrt[3]{300m^4n^8p^4}}{\sqrt[3]{125p^8}}$ which would further simplify to $\Large \frac{n^2\sqrt[3]{300m^4p^4}}{5p^2}$
At this point the formula would simplified as far as it can be, would this be correct?