Why is $n^0 = 1$? Why is any number to the zeroeth power equal to 1?  I would think it would be equal to zero, since nothing multiplied by nothing is, well, I would think 0.  But it is 1?
Examples:
$(-5)^0 = 1$;
$0^0 = 1$;
$5^0 = 1$;

Expanding on what has already been said, I want to emphasize that $a^0=1$ is a convention. There is no computation to be made, because there is no obvious meaning to "multiply with itself zero times". 
The reason why the convention is reasonable is what has been mentioned by Thorben's answer and Gregory's comment: the relation $a^{m+n}=a^ma^n$ is so nice that it makes sense to extend to the rest of the integers. Once you have $a^0=1$, you also get $a^{-n}a^n=a^{n-n}=1$, so $a^{-n}=1/a^n$. 
