$\begin{array}{l} {a^{m} \cdot a^{n}=a^{m+n}} \\ \dfrac{a^{m}}{a^{n}}=a^{m-n} \\ a^{n}\cdot b^{n}=({ab})^{n} \\ (a^{n})^{m}=a^{n\cdot m} \\ \\ \textbf{Gegeben:} \\ {a=2 \qquad b=3 \qquad m=3 \qquad n=2}\\ \\ \textbf{Rechnung:} \\ {2^{3} \cdot 2^{2}=2^{3+2}=2^{5}=32}\\ 2^{3}:2^{2}=\dfrac{2^{3}}{2^{2}}=2^{3-2}=2^{1}=2\\ 2^{2}\cdot 3^{2}=(2\cdot3)^{2}= 6^{2}={36} \\ (2^{2})^{3}=2^{2\cdot 3} = 2^{6}={64} \end{array}$