Beispiel Nr: 07
${a^{m} \cdot a^{n}=a^{m+n}} \quad \dfrac{a^{m}}{a^{n}}=a^{m-n} \quad a^{n}\cdot b^{n}=({ab})^{n} \quad (a^{n})^{m}=a^{n\cdot m} \\ \\ \textbf{Gegeben:} \\ {a=\frac{1}{3} \qquad b=\frac{2}{5} \qquad m=2 \qquad n=3}\\ \\ \textbf{Rechnung:} \\ {\left(\frac{1}{3}\right)^{2} \cdot \left(\frac{1}{3}\right)^{3}=\left(\frac{1}{3}\right)^{2+3}=\left(\frac{1}{3}\right)^{5}=0,00412}\\ \left(\frac{1}{3}\right)^{2}:\left(\frac{1}{3}\right)^{3}=\dfrac{\left(\frac{1}{3}\right)^{2}}{\left(\frac{1}{3}\right)^{3}}=\left(\frac{1}{3}\right)^{2-3}=\left(\frac{1}{3}\right)^{-1}=3\\ \left(\frac{1}{3}\right)^{3}\cdot \left(\frac{2}{5}\right)^{3}=(\frac{1}{3}\cdot\frac{2}{5})^{3}= \left(\frac{2}{15}\right)^{3}={0,00237} \\ (\left(\frac{1}{3}\right)^{3})^{2}=\left(\frac{1}{3}\right)^{3\cdot 2} = \left(\frac{1}{3}\right)^{6}={0,00137} $