$\begin{array}{l} {a^{m} \cdot a^{n}=a^{m+n}} \\ \dfrac{a^{m}}{a^{n}}=a^{m-n} \\ a^{n}\cdot b^{n}=({ab})^{n} \\ (a^{n})^{m}=a^{n\cdot m} \\ \\ \textbf{Gegeben:} \\ {a=-2 \qquad b=-3 \qquad m=2 \qquad n=1}\\ \\ \textbf{Rechnung:} \\ {\left(-2\right)^{2} \cdot \left(-2\right)^{1}=\left(-2\right)^{2+1}=\left(-2\right)^{3}=-8}\\ \left(-2\right)^{2}:\left(-2\right)^{1}=\dfrac{\left(-2\right)^{2}}{\left(-2\right)^{1}}=\left(-2\right)^{2-1}=\left(-2\right)^{1}=-2\\ \left(-2\right)^{1}\cdot \left(-3\right)^{1}=(\left(-2\right)\cdot\left(-3\right))^{1}= 6^{1}={6} \\ (\left(-2\right)^{1})^{2}=\left(-2\right)^{1\cdot 2} = \left(-2\right)^{2}={4} \end{array}$