Definition:Power (Algebra)/Power of Zero

Definition
Let $r \in \R$ be a real number.

(This includes the situation where $r \in \Z$ or $r \in \Q$.)

When $x=0$, $x^r$ is defined as follows:


 * $0^r = \begin{cases}

1 & : r = 0 \\ 0 & : r > 0 \\ \text{Undefined} & : r < 0 \\ \end{cases}$

This takes account of the awkward case $0^0$: it is "generally accepted" that $0^0 = 1$ as this convention agrees with certain general results which would otherwise need a special case.

Also see

 * Zero to the Zeroth Power