\begin{definition}[Definition:Power-Associative Operation]
Let $\circ$ be a binary operation.
Then $\circ$ is defined as being '''power-associative on $S$''' {{iff}}:
:$\forall x \in S: \paren {x \circ x} \circ x = x \circ \paren {x \circ x}$
\end{definition}