$\begin{array}{l} {a^{m} \cdot a^{n}=a^{m+n}} \\ \dfrac{a^{m}}{a^{n}}=a^{m-n} \\ a^{n}\cdot b^{n}=({ab})^{n} \\ (a^{n})^{m}=a^{n\cdot m} \\ \\ \textbf{Gegeben:} \\ {a=-2 \qquad b=-4 \qquad m=2 \qquad n=2}\\ \\ \textbf{Rechnung:} \\ {\left(-2\right)^{2} \cdot \left(-2\right)^{2}=\left(-2\right)^{2+2}=\left(-2\right)^{4}=16}\\ \left(-2\right)^{2}:\left(-2\right)^{2}=\dfrac{\left(-2\right)^{2}}{\left(-2\right)^{2}}=\left(-2\right)^{2-2}=\left(-2\right)^{0}=1\\ \left(-2\right)^{2}\cdot \left(-4\right)^{2}=(\left(-2\right)\cdot\left(-4\right))^{2}= 8^{2}={64} \\ (\left(-2\right)^{2})^{2}=\left(-2\right)^{2\cdot 2} = \left(-2\right)^{4}={16} \end{array}$