Prove that any number raised to the 0'th power equals 1

(a number) ^to the 'A' power, divided by (the same number) ^to the 'B' power =

(the same number) ^ (A - B) power

If 'A' = 'B', then the numerator and the denominator are both

(the same number) ^to the same power,

and since (A - B = 0), the quotient is (the same number) ^to the (0) power.

But a fraction with the same thing in the numerator and the denominator is '1 '.

qed