What is 2 to the power of 0 why?

Answer 1

20 = 1

Consider what is the value of 2a ÷ 2a? Any number divided by itself is 1. Thus:

2a ÷ 2a = 1

The law of indices says that when dividing, they are subtracted, for example:

25 ÷ 22 = (2 x 2 x 2 x 2 x 2) ÷ (2 x 2) = 2 x 2 x 2 = 23 = 25-2

So 2a ÷ 2a is (also):

2a ÷ 2a = 2a-a = 20

Since any number subtracted from itself is 0 (= a - a). This must have the same value as before, thus:

20 = 1

The 2 above can be replaced by any number x which means that any number to the power 0 is 1:

x0 = 1