2013-2014/3e/Nombres_Calculs/Puissance/fiches_exo/puissances_1.tex

\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
\usepackage{multicol}

% Title Page
\title{Puissances - Exercices}
\author{}
\date{}

\fancyhead[L]{Troisième}
\fancyhead[C]{\Thetitle}
\fancyhead[R]{\thepage}


\begin{document}
\thispagestyle{fancy}

\begin{Exo}
    \begin{enumerate}
        \item Completer les formules suivantes
            \begin{eqnarray*}
                a^m \times a^n = \parbox{2cm}{\dotfill} \hspace{1cm} \left( a^n \right)^m  =\parbox{2cm}{\dotfill} \\[0.5cm]
                a^{-n} = \parbox{3cm}{\dotfill} = \frac{1}{a^{\parbox{1cm}{\dotfill}}}
            \end{eqnarray*}
            \vspace{-1cm}
        \item Mettre les nombres suivants sous la forme $a^n$
            \begin{multicols}{2}
                \begin{eqnarray*}
                    2^{13} \times 2^5 = \parbox{1cm}{\dotfill}    =\parbox{1cm}{\dotfill}   \\[0.5cm]
                    6^{3} \times 6^5 = \parbox{1cm}{\dotfill}     = \parbox{1cm}{\dotfill}  \\[0.5cm]
                    5^{10} \times 5^{-7} = \parbox{1cm}{\dotfill} =  \parbox{1cm}{\dotfill} \\[0.5cm]
                    10^{-5} \times 10^6 = \parbox{1cm}{\dotfill}    =  \parbox{1cm}{\dotfill} \\[0.5cm]
                    11^{-33} \times 11^9 = \parbox{1cm}{\dotfill} = \parbox{1cm}{\dotfill} \\[0.5cm]
                    2^4 \times 2^5 \times 2^7 =  \parbox{1cm}{\dotfill} = \parbox{1cm}{\dotfill} 
                \end{eqnarray*}
                \columnbreak
                \begin{eqnarray*}
                    2^9 \times \frac{1}{2^6} =  \parbox{1cm}{\dotfill} = \parbox{1cm}{\dotfill} \\[0.5cm]
                    6^5 \times \frac{1}{6^9} =  \parbox{1cm}{\dotfill} = \parbox{1cm}{\dotfill} \\[0.5cm]
                    5^6\times \frac{1}{5^2} =  \parbox{1cm}{\dotfill} = \parbox{1cm}{\dotfill} \\[0.5cm]
                    10^{-4} \times 10^5 \times \frac{1}{10^7} =  \parbox{1cm}{\dotfill} = \parbox{1cm}{\dotfill}  \\[0.5cm]
                    \left( 3^4 \right)^6 = \parbox{1cm}{\dotfill} = \parbox{1cm}{\dotfill} 
                \end{eqnarray*}
            \end{multicols}
            
            
    \end{enumerate}
\end{Exo}

\vspace{-1cm}
\begin{Exo}
    \begin{enumerate}
        \item Réécrire avec des multiplications puis mettre sous la forme $a^n$

                \begin{eqnarray*}
                    \frac{2^5}{2^3} =  \frac{\parbox{3cm}{\dotfill}}{\parbox{3cm}{\dotfill}} = 2^{\parbox{1cm}{\dotfill}} \\[0.5cm]
                    \frac{10^4}{10^2} =  \frac{\parbox{3cm}{\dotfill}}{\parbox{3cm}{\dotfill}} = 2^{\parbox{1cm}{\dotfill}} \\[0.5cm]
                    \frac{3^4}{3^5} =  \frac{\parbox{3cm}{\dotfill}}{\parbox{3cm}{\dotfill}} = 2^{\parbox{1cm}{\dotfill}}
                \end{eqnarray*}
                \begin{eqnarray*}
                    \frac{2^4}{2^5} =  \frac{\parbox{3cm}{\dotfill}}{\parbox{3cm}{\dotfill}} = 2^{\parbox{1cm}{\dotfill}} \\[0.5cm]
                \end{eqnarray*}
            \vspace{-1cm}
        \item Donner une idée pour completer la formule suivante
            \begin{eqnarray*}
                \frac{a^n}{a^m} & = & a^{\parbox{1cm}{\dotfill}}
            \end{eqnarray*}
            
    \end{enumerate}


\end{Exo}
%\eject

\begin{Exo}
    Mettre les expressions suivantes sous la forme $a^n$

            \begin{multicols}{3}
                \begin{eqnarray*}
                    \frac{2^5 \times 2^7}{2^5} \\[0.5cm]
                    \frac{2^7 \times 2^2}{2^9} \\[0.5cm]
                    \frac{2^5}{ 2^4 \times 2^5} \\[0.5cm]
                    \frac{2^{-5} \times 2^{3}}{2^5} \\[0.5cm]
                    \frac{2^5 \times 2^9}{2^2 \times 2^6} \\[0.5cm]
                    \frac{2^{-5} \times 2^3}{2^{-5}}
                \end{eqnarray*}
                \columnbreak
                \begin{eqnarray*}
                    \frac{10^4 \times 10^8}{10^2} \\[0.5cm]
                    \frac{10^8 \times 10^7}{10^{15}} \\[0.5cm]
                    \frac{10^6}{ 10^3 \times 10^5} \\[0.5cm]
                    \frac{10^{-5} \times 10^{3} \times 10^6}{10^{33}} \\[0.5cm]
                    \frac{10^5 \times 10^5}{10 \times 10^4} \\[0.5cm]
                    \frac{10^{-5} \times 10^3}{10^{-5} \times 10^4 \times 10^{-2}}
                \end{eqnarray*}
                \columnbreak
                \begin{eqnarray*}
                    \frac{5^5 \times 5^2}{5^2} \\[0.5cm]
                    \frac{3^5 \times 3^5}{3^{-5} \times 3^5} \\[0.5cm]
                    \frac{8^3 \times 8^{-7}}{8^5} \\[0.5cm]
                    \frac{13^5 \times 13^3}{13} \\[0.5cm]
                    \frac{1^5 \times 1^7}{1^5} \\[0.5cm]
                    \frac{21^5 \times 21^7 \times 21^5}{21^5}
                \end{eqnarray*}
            \end{multicols}

\end{Exo}

\begin{Exo}
    \exo{10p106}
\end{Exo}


\end{document}

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