I was playing a bit whit exponents. I maybe found a working formula for calculating $n^y$ if you know $n^x$. The formula may already be discovered, but the formula I found is: $$ (n^x)^\frac{y}{x} = n^y $$ Ok, so the formula should work if $n,x,y \in \mathbb N$
I am not sure if it does work whit negative and decimal numbers tho.
Ok, my questions are:
1. Can the formula be used whit decimal, and negative numbers (x,y,n)
2. Can you prove that the formula works if $x,y,n \in \mathbb N$, if it is possible also for $x,y,n \in \mathbb Q$, $x,y,n \in \mathbb R$ and $x,y,n \in \mathbb Z$.