Why anything power 0 is one?

Answer 1

This is related to the fact that one is the identity element of multiplication. If nothing is multiplied, the result must be zero.

Look at the following sequence:

103 = 1000

102 = 100

101 = 10

100 = ???

On the left, the exponent decreases one at a time. On the right, the numbers decrease every time by a factor of 10. So, you would expect the missing number on the right to be a one.

Yet another way to look at this is that certain rules, like xa times xb = xa+b, maintain their validity for more cases, if you defined x0 = 1. For example, 100 times 103 should be equal to103. This is only possible if you define 100 = 1.