I have just read a very basic introduction to the RSA algorithm.
Let's suppose my two prime numbers are $p=29$ and $q=37$. Then $n=pq=1073$ and $e=5$. $n$ and $e$ are public.
If I want to send the letter U, which is n°21 in the alphabet, I would send $21^e$ (mod $1073$) that is $263$.
Normally I should calculate $(21^e)^d$, where $d=605$. But why not calculate $(263)^{1/5}$ ?