Factor 1
Any number multiplied by the factor 1 is that number.
Explanation
Every number multiplied by 1 stays unchanged. That makes the table of 1 so simple. But there is more than that. The meaning of exponentiation is "multiply the factor 1 so often with the base, as indicated by the exponent", so
a3 = 1·a·a·a
a2 = 1·a·a
a1 = 1·a
a0 = 1
Exponent zero indicates that the factor 1 is not to be multiplied with the base, and as a result only 1 is left. This notation produces 00 ≝ 1 and that is just fine.