Zero to the Power of Zero/Exponential of Zero

Example of Zero to the Power of Zero

By Exponential of Zero:

$\exp 0 = 1$

From Power Series Expansion for Exponential Function

$\exp x = \dfrac {x^0} {0!} + \dfrac {x^1} {1!} + \dfrac {x^2} {2!} + \cdots$

For these theorems to be consistent, it is necessary that:

$\exp 0 = 1 = \dfrac {0^0} {0!} + 0 + 0 + \cdots$

which holds only if $0^0 = 1$.