Beispiel Nr: 03
${a^{m} \cdot a^{n}=a^{m+n}} \quad \dfrac{a^{m}}{a^{n}}=a^{m-n} \quad a^{n}\cdot b^{n}=({ab})^{n} \quad (a^{n})^{m}=a^{n\cdot m} \\ \\ \textbf{Gegeben:} \\ {a=2 \qquad b=3 \qquad m=2 \qquad n=2}\\ \\ \textbf{Rechnung:} \\ {2^{2} \cdot 2^{2}=2^{2+2}=2^{4}=16}\\ 2^{2}:2^{2}=\dfrac{2^{2}}{2^{2}}=2^{2-2}=2^{0}=1\\ 2^{2}\cdot 3^{2}=(2\cdot3)^{2}= 6^{2}={36} \\ (2^{2})^{2}=2^{2\cdot 2} = 2^{4}={16} $