Für alle reellen Zahlen a und b; {a\,\in \,\mathbb{R}\,\wedge a\ne 0} und {\large b\,\in \,\mathbb{R}\,\wedge b\ne 0 }
{\huge \displaystyle \begin{array}{l}{{a}^{m}}\cdot {{a}^{n}}={{a}^{m+n}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{{{a}^{m}}} {{{a}^{n}}}\,=\,{{a}^{m-n}}\\\\{{a}^{m}}\cdot {{b}^{m}}\,=\,{{\left( a\cdot b \right)}^{m}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{{{a}^{m}}}{{{b}^{m}}}\,=\,{{\left( \frac{a}{b} \right)}^{m}}\\\\{{\left( {{a}^{m}} \right)}^{n}}=\,{{a}^{m\,\cdot \,n}}\end{array} }