i only need it simplified so r and t are only written once
\({(\frac{{r}^{3m}}{{r}^{-m}{t}^{4n}})}^{\frac{1}{n}} \times {(\frac{{r}^{\frac{1}{n}}}{{t}^{\frac{2}{m}}})}^{-m}\)
if you want to know, this insanity looks like this with no latex.
{(\frac{{r}^{3m}}{{r}^{-m}{t}^{4n}})}^{\frac{1}{n}} \times {(\frac{{r}^{\frac{1}{n}}}{{t}^{\frac{2}{m}}})}^{-m}
because thats definitely easy to type.
Let's take this by stages
r3m r 4m r 4m/n
______ = _______ raising all this to 1/n = ______
r-m * t4n t 4n t 4
And
r 1/n ( t 2/m )m t 2
_____ raised to the -m = _______ = ______
t 2/m ( r 1/n ) m r m/n
So....putting all this together, we have
r 4m/n * t2 r 3m/n
_________ = ________
t4 * r m/n t 2