What is $R^0$ when $R=0$?

Question

We say that for a number $R$, $R^0 =1$, but if $R=0$ how can $R^0$ be $1$?

Answer 1

In other words, you are asking why $0^0=1$.

The answer is: Because mathematicians defined it like so.

There are reasons to do this. One reason is that this makes the binomial theorem $$(x+y)^n = \sum_{k=0}^n {n \choose k} x^{k}y^{n-k}$$

also valid when $x=-y$, or when $x=0$ or $y=0$, without having to say its invalid in that case. Especially $x=-y$ is important in this case.