How do you prove that a to the power of 0 equals 1?

Answer 1

You first define negative powers as the reciprocals of the positive powers ie x-a = 1/xa.

You have the folowing property for positive powers: xa * xb = xa+b

You extend the following property to negative powers:

So xa * x-a = x0. But by definition, xa * x-a = xa * 1/xa = 1

So x0 = 1