(related to Definition: Exponentiation in a Group)
Let \((G,\ast)\) be an group, \(x,y\in G\), and \(n,m\in\mathbb Z\) two integers. Then the calculation rules for exponentiation are:
\[\begin{array}{cl} (1)&x^nx^m=x^{n+m},\\ \end{array} \]
If the group is Abelian, then, in addition \[\begin{array}{cl} (2)&(x^n)^m=x^{nm}.\\ (3)&x^ny^n=(xy)^n.\\ (4)&\frac{x^n}{y^n}=\left(\frac xy\right)^n. \end{array} \]
Proofs: 1