$\begin{array}{l} {a^{m} \cdot a^{n}=a^{m+n}} \\ \dfrac{a^{m}}{a^{n}}=a^{m-n} \\ a^{n}\cdot b^{n}=({ab})^{n} \\ (a^{n})^{m}=a^{n\cdot m} \\ \\ \textbf{Gegeben:} \\ {a=2 \qquad b=4 \qquad m=4 \qquad n=2}\\ \\ \textbf{Rechnung:} \\ {2^{4} \cdot 2^{2}=2^{4+2}=2^{6}=64}\\ 2^{4}:2^{2}=\dfrac{2^{4}}{2^{2}}=2^{4-2}=2^{2}=4\\ 2^{2}\cdot 4^{2}=(2\cdot4)^{2}= 8^{2}={64} \\ (2^{2})^{4}=2^{2\cdot 4} = 2^{8}={256} \end{array}$