\ANG{
\begin{enumerate}
    \item Ergänze die Tabelle folgerichtig: \\ \\
    \renewcommand{\arraystretch}{2} 
    \begin{tabular}{|c|c|c|c|c|c|} \hline
        $5^2$ & $5^1$ & $5^0$ & $5^{-1}$ & $5^{-2}$ & $5^{-3}$\\ \hline
        $25$ & $5$ & & & &  \\ \hline
        \multicolumn{4}{c}{\stackrel {:5}{\rightarrow} \quad \stackrel {:5}{\rightarrow} ... \qquad \qquad}
    \end{tabular}
    \item Gib in Wurzel- und Bruchschreibweise an $\left( a \in \mathbb{R}^+ \right)$. \\ \\
    Beispiele: 
    (1) $a^{\frac 5 3} = \left( a^{\frac 1 3}\right)^5 = {\sqrt[3] a}^5 \qquad \qquad$
    (2) $a^{-\frac 2 3} = \D\frac 1 {a^{\frac 2 3}} = \D\frac 1 {{\sqrt[3] a}^2}$ \\ \\
    (3) $ a^{\frac 1 2}\qquad \qquad \qquad$ 
    (4) $a^{\frac 7 4} \qquad \qquad \qquad $ 
    (5) $a^{-\frac4 5} $
    \item Gib in Potenzschreibweise an $\left( b \in \mathbb{R}^+ \right)$. \\ \\
    Beispiele: 
    (1) $\sqrt[3]{b^2} = \left( b^2 \right)^{\frac 1 3} = b^{\frac 2 3}\qquad \qquad$
    (2) $\D\frac 7 {\sqrt[2]b^5} = \D\frac 7 {\left( \sqrt[2] b\right)^5} = \D\frac 7 {b^{\frac 5 2}}
         = 7 \cdot b^{-\frac 5 2}$ \\ \\
    (3) $ \sqrt[4]{b^3} \qquad \qquad \qquad$
    (4) $\D\frac 2 {\sqrt b} \qquad \qquad \qquad$
    (5) $\D\frac 3 {\sqrt[5]{b^2}}$
\end{enumerate}
}\LSG{ 
\begin{enumerate}
    \item Ergänze die Tabelle folgerichtig: \\ \\
    \renewcommand{\arraystretch}{2} 
    \begin{tabular}{|c|c|c|c|c|c|} \hline
        $5^2$ & $5^1$ & $5^0$ & $5^{-1}$ & $5^{-2}$ & $5^{-3}$\\ \hline
        $25$ & $5$ & $1$ & $\D\frac 1 5$ & $\D\frac 1 {25}$ & $\D\frac 1 {125}$  \\ \hline
    \end{tabular} \\
    \item 
    (3) $a^{\frac 1 2} = \sqrt[2] a $ \\ \\
    (4) $a^{\frac 7 4} = \left(a^{\frac 1 4} \right)^7 = \sqrt[4]a^7 $ \\ \\
    (5) $a^{-\frac 4 5} = \D\frac 1 {a^{\frac 4 5}} = \D\frac 1 {\sqrt[5] a^4} $
    \item
    (3) $ \sqrt[4]{b^3} = \left( b^3 \right)^{\frac 1 4} = b^{\frac 3 4}$ \\ \\
    (4) $\D\frac 2 {\sqrt b} = \D\frac 2 {b^{\frac 1 2}} = 2 \cdot b^{-\frac 1 2}$ \\ \\
    (5) $\D\frac 3 {\sqrt[5]{b^2}} = \D\frac 3 {b^{\frac 2 5}} = 3 \cdot b^{-\frac 2 5}$
\end{enumerate}
}