指数法則〜整数編〜

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かけ算は足し算に

この問題へのリンクはこちら(右クリックで保存)

\def\MondaiB{a}
\def\MondaiIl{m}
\def\MondaiIr{n}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\begin{align*}
\colMM{red}{かけ算は } & \colMM{red}{  \ 足し算に}\\
\MondaiB^{\MondaiIl} \colBX{mistyrose}{$\times$} \MondaiB^{\MondaiIr} &= \MondaiB\,^{\MondaiIl \colBX{mistyrose}{$\scriptsize +$} \MondaiIr}\\
\colMM{red}{底が同じ }\\
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan

【解答】

\def\MondaiB{3}
\def\MondaiIl{5}
\def\MondaiIr{-2}
\def\KeisanI{3}
\def\Kotae{27}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\begin{align*}
\colMM{red}{かけ算は } & \colMM{red}{  \ 足し算に}\\
\MondaiB^{\MondaiIl} \colBX{mistyrose}{$\times$} \MondaiB^{\MondaiIr} &= \MondaiB\,^{\MondaiIl \colBX{mistyrose}{$\scriptsize +$} (\MondaiIr)}\\
\colMM{red}{底が同じ }\\
&= 3^{\KeisanI}\\
\\
&= \Kotae
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan

この問題へのリンクはこちら(右クリックで保存)

\def\MondaiB{a}
\def\MondaiIl{m}
\def\MondaiIr{n}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\begin{align*}
\colMM{red}{かけ算は } & \colMM{red}{  \ 足し算に}\\
\MondaiB^{\MondaiIl} \colBX{mistyrose}{$\times$} \MondaiB^{\MondaiIr} &= \MondaiB\,^{\MondaiIl \colBX{mistyrose}{$\scriptsize +$} \MondaiIr}\\
\colMM{red}{底が同じ }\\
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan

【解答】

\def\MondaiB{3}
\def\MondaiIl{4}
\def\MondaiIr{-2}
\def\KeisanI{2}
\def\Kotae{9}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\begin{align*}
\colMM{red}{かけ算は } & \colMM{red}{  \ 足し算に}\\
\MondaiB^{\MondaiIl} \colBX{mistyrose}{$\times$} \MondaiB^{\MondaiIr} &= \MondaiB\,^{\MondaiIl \colBX{mistyrose}{$\scriptsize +$} (\MondaiIr)}\\
\colMM{red}{底が同じ }\\
&= 3^{\KeisanI}\\
\\
&= \Kotae
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan

わり算は引き算に

この問題へのリンクはこちら(右クリックで保存)

\def\MondaiB{a}
\def\MondaiIl{m}
\def\MondaiIr{n}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\begin{align*}
\colMM{red}{わり算は } & \colMM{red}{  \ ひき算に}\\
\dfrac{\MondaiB^{\MondaiIl}}{\MondaiB^{\MondaiIr}} = \MondaiB^{\MondaiIl} \colBX{mistyrose}{$\div$} \MondaiB^{\MondaiIr} &= \MondaiB\,^{\MondaiIl \colBX{mistyrose}{$\scriptsize -$} \MondaiIr}\\
\colMM{red}{底が同じ }\\
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan

【解答】

\def\MondaiB{3}
\def\MondaiIl{5}
\def\MondaiIr{-2}
\def\KeisanI{7}
\def\Kotae{\ \color{lightgray}{= 2187}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\begin{align*}
\colMM{red}{わり算は } & \colMM{red}{  \ ひき算に}\\
\dfrac{\MondaiB^{\MondaiIl}}{\MondaiB^{\MondaiIr}} = \MondaiB^{\MondaiIl} \colBX{mistyrose}{$\div$} \MondaiB^{\MondaiIr} &= \MondaiB\,^{\MondaiIl \colBX{mistyrose}{$\scriptsize -$} (\MondaiIr)}\\
\colMM{red}{底が同じ }\\
&= 3^{\KeisanI}\\
\\
& \Kotae
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan

この問題へのリンクはこちら(右クリックで保存)

\def\MondaiB{a}
\def\MondaiIl{m}
\def\MondaiIr{n}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\begin{align*}
\colMM{red}{わり算は } & \colMM{red}{  \ ひき算に}\\
\dfrac{\MondaiB^{\MondaiIl}}{\MondaiB^{\MondaiIr}} = \MondaiB^{\MondaiIl} \colBX{mistyrose}{$\div$} \MondaiB^{\MondaiIr} &= \MondaiB\,^{\MondaiIl \colBX{mistyrose}{$\scriptsize -$} \MondaiIr}\\
\colMM{red}{底が同じ }\\
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan

【解答】

\def\MondaiB{10}
\def\MondaiIl{-3}
\def\MondaiIr{2}
\def\KeisanI{-5}
\def\Kotae{\ =\dfrac{1}{10^{5}}\\\\ &= \dfrac{1}{100000} }
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\begin{align*}
\colMM{red}{わり算は } & \colMM{red}{  \ ひき算に}\\
\dfrac{\MondaiB^{\MondaiIl}}{\MondaiB^{\MondaiIr}} = \MondaiB^{\MondaiIl} \colBX{mistyrose}{$\div$} \MondaiB^{\MondaiIr} &= \MondaiB\,^{\MondaiIl \colBX{mistyrose}{$\scriptsize -$} \MondaiIr}\\
\colMM{red}{底が同じ }\\
&= \MondaiB^{\KeisanI}\\
\\
& \Kotae
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan

指数が並んだら「かける」

この問題へのリンクはこちら(右クリックで保存)

【解答】

\def\MondaiB{3}
\def\MondaiIa{5}
\def\MondaiIb{-2}
\def\KakkoLl{}\def\KakkoLr{}
\def\KakkoRl{(}\def\KakkoRr{)}
\def\KeisanI{-10}
\def\Kotae{\\&\colMM{lightgray}{  \Darr 計算してみた}\\&\color{lightgray}=\dfrac{1}{3^{10}} = \dfrac{1}{59049}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\begin{align*}
\colMM{red}{指数が並んだ} & \colMM{red}{   かける!}\\
\left(\MondaiB^{\colBX{mistyrose}{$\scriptsize\MondaiIa$}}\right)^{\colBX{mistyrose}{$\scriptsize\MondaiIb$}} &= \MondaiB^{\colBX{mistyrose}{$\scriptsize\KakkoLl\MondaiIa\KakkoLr \times \KakkoRl\MondaiIb\KakkoRr$}}\\
\\
&= \MondaiB^{\KeisanI}
\Kotae
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan

この問題へのリンクはこちら(右クリックで保存)

【解答】

\def\MondaiB{3}
\def\MondaiIa{-2}
\def\MondaiIb{4}
\def\KakkoLl{}\def\KakkoLr{}
\def\KakkoRl{}\def\KakkoRr{}
\def\KeisanI{-8}
\def\Kotae{\\&\colMM{lightgray}{  \Darr 計算してみた}\\&\color{lightgray}=\dfrac{1}{3^{8}} = \dfrac{1}{6561}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\begin{align*}
\colMM{red}{指数が並んだ} & \colMM{red}{   かける!}\\
\left(\MondaiB^{\colBX{mistyrose}{$\scriptsize\MondaiIa$}}\right)^{\colBX{mistyrose}{$\scriptsize\MondaiIb$}} &= \MondaiB^{\colBX{mistyrose}{$\scriptsize\KakkoLl\MondaiIa\KakkoLr \times \KakkoRl\MondaiIb\KakkoRr$}}\\
\\
&= \MondaiB^{\KeisanI}
\Kotae
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan

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