How does it work?
Probably all lies but thanks.
0^0=1 what sort of maths is that? 
“0^0” in mathematics refers to “1 infinitesimal times infinity”, which equals 1.
Fractional exponents such as 1/n refers to n being the number of times the solution must be multiplied times itself in order to get the root number.
For example;
2^(1/2) = x, means that if you multiple x times itself 2 times you will get 2.
3^(1/3) = x, means that if you multiple x times itself 3 times you will get 3.
But if the root number is a fraction, x will always be larger than the root because a fraction times itself would always be smaller than itself. So as the root fraction in “n^n = x” gets smaller, x gets larger. And the result makes a graph that looks something like this;
James 0^0=1 is not actually factual but thanks for contributing to this thread none the less. 
Actually no james taking a route of 0 and squaring it leads to the answer 1 axiomatically because 1=1 based on the same ZFT axiom that 1+1 always will equal 2, this makes all the other powers work, and is called the power series because according to that ZFT the factors only work if there are zero factors in that theory. It’s not so much that 1^1=1 or that 0^0=1 it’s more the fact that the power rules only work if 0=0 and likewise the power rules only work if we introduce the axiom that 0^0=1 and hence 0^-1 is…
Essentially the derivative of a negative is a negative, so d/dx of x^-2 is of course nx^-1 where n is 1.
Except in hyperreals, formal mathematics doesn’t recognize the distinction between absolute zero and one infinitesimal. Absolute zero cannot exist any more than an infinite real number can exist. Thus;
“as n goes to infinity, (1/n)^(1/n) approaches 1”.
Or in first cardinal mathematics, “0^0 = 1”.
Complain about it all you like, but as long as 1+1=2, it will be true.
Complain about Cantor?
I can’tor. 