I always found a good way of understanding it was:
x^n * x^p = x^(n+p)
if p = 0, then we need it to come out x^n * x^0 = x^(n+0) = x^n
This can only work if x^0 is 1 (a number multiplied by 1 is itself).
Any help? I'm sure there are many other ways to show it - it just depends which works for you
