why does 0 to the power of 0 equal 1?

Question

why does 0 to the power of 0 equal 1?

In: 97

Answer 1

The ELI5 answer is “beacuse mathematicians decide it was simplest if it did.” Any real answer is going to need calculus or more complex math to demonstrate

Here is how I think of it: x^0 = x^n * x^-n = x^n / x^n = 1 for all non zero cases because 0/0 is undefined. However we can use L’Hopital’s rule to determine it converges to a specific value. The first iteration of the rule transforms the equation into x*n / x*n, which is still undefined. The second itteration transforms it to n/n which is 1. So because the numerator and denominator are growing at the same rate, 0^n / 0^n = 1, therefore 0^0 = 1.