120 lines
4.8 KiB
TeX
120 lines
4.8 KiB
TeX
\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/Archive/2013-2014/tools/style/classExo}
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\usepackage{multicol}
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% Title Page
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\title{Puissances - Exercices}
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\author{}
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\date{}
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\fancyhead[L]{Troisième}
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\fancyhead[C]{\Thetitle}
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\fancyhead[R]{\thepage}
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\begin{document}
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\thispagestyle{fancy}
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\begin{Exo}
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\begin{enumerate}
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\item Completer les formules suivantes
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\begin{eqnarray*}
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a^m \times a^n = \parbox{2cm}{\dotfill} \hspace{1cm} \left( a^n \right)^m =\parbox{2cm}{\dotfill} \\[0.5cm]
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a^{-n} = \parbox{3cm}{\dotfill} = \frac{1}{a^{\parbox{1cm}{\dotfill}}}
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\end{eqnarray*}
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\vspace{-1cm}
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\item Mettre les nombres suivants sous la forme $a^n$
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\begin{multicols}{2}
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\begin{eqnarray*}
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2^{13} \times 2^5 = \parbox{1cm}{\dotfill} =\parbox{1cm}{\dotfill} \\[0.5cm]
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6^{3} \times 6^5 = \parbox{1cm}{\dotfill} = \parbox{1cm}{\dotfill} \\[0.5cm]
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5^{10} \times 5^{-7} = \parbox{1cm}{\dotfill} = \parbox{1cm}{\dotfill} \\[0.5cm]
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10^{-5} \times 10^6 = \parbox{1cm}{\dotfill} = \parbox{1cm}{\dotfill} \\[0.5cm]
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11^{-33} \times 11^9 = \parbox{1cm}{\dotfill} = \parbox{1cm}{\dotfill} \\[0.5cm]
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2^4 \times 2^5 \times 2^7 = \parbox{1cm}{\dotfill} = \parbox{1cm}{\dotfill}
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\end{eqnarray*}
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\columnbreak
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\begin{eqnarray*}
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2^9 \times \frac{1}{2^6} = \parbox{1cm}{\dotfill} = \parbox{1cm}{\dotfill} \\[0.5cm]
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6^5 \times \frac{1}{6^9} = \parbox{1cm}{\dotfill} = \parbox{1cm}{\dotfill} \\[0.5cm]
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5^6\times \frac{1}{5^2} = \parbox{1cm}{\dotfill} = \parbox{1cm}{\dotfill} \\[0.5cm]
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10^{-4} \times 10^5 \times \frac{1}{10^7} = \parbox{1cm}{\dotfill} = \parbox{1cm}{\dotfill} \\[0.5cm]
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\left( 3^4 \right)^6 = \parbox{1cm}{\dotfill} = \parbox{1cm}{\dotfill}
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\end{eqnarray*}
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\end{multicols}
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\end{enumerate}
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\end{Exo}
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\vspace{-1cm}
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\begin{Exo}
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\begin{enumerate}
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\item Réécrire avec des multiplications puis mettre sous la forme $a^n$
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\begin{eqnarray*}
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\frac{2^5}{2^3} = \frac{\parbox{3cm}{\dotfill}}{\parbox{3cm}{\dotfill}} = 2^{\parbox{1cm}{\dotfill}} \\[0.5cm]
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\frac{10^4}{10^2} = \frac{\parbox{3cm}{\dotfill}}{\parbox{3cm}{\dotfill}} = 2^{\parbox{1cm}{\dotfill}} \\[0.5cm]
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\frac{3^4}{3^5} = \frac{\parbox{3cm}{\dotfill}}{\parbox{3cm}{\dotfill}} = 2^{\parbox{1cm}{\dotfill}}
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\end{eqnarray*}
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\begin{eqnarray*}
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\frac{2^4}{2^5} = \frac{\parbox{3cm}{\dotfill}}{\parbox{3cm}{\dotfill}} = 2^{\parbox{1cm}{\dotfill}} \\[0.5cm]
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\end{eqnarray*}
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\vspace{-1cm}
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\item Donner une idée pour completer la formule suivante
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\begin{eqnarray*}
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\frac{a^n}{a^m} & = & a^{\parbox{1cm}{\dotfill}}
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\end{eqnarray*}
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\end{enumerate}
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\end{Exo}
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%\eject
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\begin{Exo}
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Mettre les expressions suivantes sous la forme $a^n$
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\begin{multicols}{3}
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\begin{eqnarray*}
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\frac{2^5 \times 2^7}{2^5} \\[0.5cm]
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\frac{2^7 \times 2^2}{2^9} \\[0.5cm]
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\frac{2^5}{ 2^4 \times 2^5} \\[0.5cm]
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\frac{2^{-5} \times 2^{3}}{2^5} \\[0.5cm]
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\frac{2^5 \times 2^9}{2^2 \times 2^6} \\[0.5cm]
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\frac{2^{-5} \times 2^3}{2^{-5}}
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\end{eqnarray*}
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\columnbreak
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\begin{eqnarray*}
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\frac{10^4 \times 10^8}{10^2} \\[0.5cm]
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\frac{10^8 \times 10^7}{10^{15}} \\[0.5cm]
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\frac{10^6}{ 10^3 \times 10^5} \\[0.5cm]
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\frac{10^{-5} \times 10^{3} \times 10^6}{10^{33}} \\[0.5cm]
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\frac{10^5 \times 10^5}{10 \times 10^4} \\[0.5cm]
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\frac{10^{-5} \times 10^3}{10^{-5} \times 10^4 \times 10^{-2}}
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\end{eqnarray*}
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\columnbreak
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\begin{eqnarray*}
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\frac{5^5 \times 5^2}{5^2} \\[0.5cm]
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\frac{3^5 \times 3^5}{3^{-5} \times 3^5} \\[0.5cm]
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\frac{8^3 \times 8^{-7}}{8^5} \\[0.5cm]
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\frac{13^5 \times 13^3}{13} \\[0.5cm]
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\frac{1^5 \times 1^7}{1^5} \\[0.5cm]
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\frac{21^5 \times 21^7 \times 21^5}{21^5}
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\end{eqnarray*}
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\end{multicols}
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\end{Exo}
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\begin{Exo}
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\exo{10p106}
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\end{Exo}
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\end{document}
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%%% Local Variables:
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%%% TeX-master: "master"
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%%% End:
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