# Definition:Power of Element/Monoid/Invertible Element

Let $\struct {S, \circ}$ be a monoid whose identity element is $e$.
Let $b \in S$ be invertible for $\circ$.
Let $n \in \Z$.
The definition $b^n = \map {\circ^n} b$ as the $n$th power of $b$ in $\left({S, \circ}\right)$ can be extended to include the inverse of $b$:
$b^{-n} = \paren {b^{-1} }^n$