$\begin{array}{l} {a^{m} \cdot a^{n}=a^{m+n}} \\ \dfrac{a^{m}}{a^{n}}=a^{m-n} \\ a^{n}\cdot b^{n}=({ab})^{n} \\ (a^{n})^{m}=a^{n\cdot m} \\ \\ \textbf{Gegeben:} \\ {a=4 \qquad b=3 \qquad m=2 \qquad n=3}\\ \\ \textbf{Rechnung:} \\ {4^{2} \cdot 4^{3}=4^{2+3}=4^{5}=1,02\cdot 10^{3}}\\ 4^{2}:4^{3}=\dfrac{4^{2}}{4^{3}}=4^{2-3}=4^{-1}=\frac{1}{4}\\ 4^{3}\cdot 3^{3}=(4\cdot3)^{3}= 12^{3}={1,73\cdot 10^{3}} \\ (4^{3})^{2}=4^{3\cdot 2} = 4^{6}={4,1\cdot 10^{3}} \end{array}$