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