exponentiation - What is 0 raised to 0 ???!!!!

I have read many articles on this confusion but i am still confused...

My simple question is -

What is $0^0$?

What is the present agreement to this?

I feel that it should be 1 as anything to the power zero is one....

I am currently a school student so i would like a more of a school based answer..

So incase it comes in my exam i should know what to write:)

Answer

$0^0$ is most often undefined. The reason is that it is not possible to define it in a good enough way. Notice the following examples:

$0^x$

Whenever $x \neq 0$ then this expression should equal to 0. However

$x^0$

should be $1$ whenever $x\neq 0$. Thus, if we define $0^0$ to either $0$ or $1$ then we get problems with these functions not being continous (without jumps if you plot them) where they are defined, which is why we keep $0^0$ undefined in most cases.