گام به گام کاردرکلاس صفحه 87 درس 7 ریاضی هفتم (توان و جذر)

\(\begin{array}{l}{2^5} + {3^2} = 32 + 9 = 41\\ - - - - - - - - - - - - - - - \\{2^5} \times {3^2} = 32 \times 9 = 288\\ - - - - - - - - - - - - - - - \\{2^5} - {3^2} = 32 - 9 = 23\\ - - - - - - - - - - - - - - - \\{2^5} \div 8 = 32 \div 8 = 4\\ - - - - - - - - - - - - - - - \\{\left( {\frac{1}{2}} \right)^2} + \frac{3}{8} = \frac{1}{4} + \frac{3}{8} = \frac{2}{8} + \frac{3}{8} = \frac{5}{8}\\ - - - - - - - - - - - - - - - \\{5^2} - 5 \times 2 = 25 - 10 = 15\\ - - - - - - - - - - - - - - - \\{\left( {\frac{5}{2}} \right)^2} - {\left( {\frac{2}{5}} \right)^2} = \frac{{25}}{4} - \frac{4}{{25}} = \\\\\frac{{625 - 16}}{{100}} = \frac{{609}}{{100}}\\ - - - - - - - - - - - - - - - \\\frac{1}{2} + {\left( {\frac{1}{2}} \right)^2} + {\left( {\frac{1}{2}} \right)^3} = \frac{1}{2} + \frac{1}{4} + \frac{1}{8} = \\\\\frac{4}{8} + \frac{2}{8} + \frac{1}{8} = \frac{{4 + 2 + 1}}{8} = \frac{7}{8}\\ - - - - - - - - - - - - - - - \\{2^4} - {3^3} + {1^5} = 16 - 27 + 1 = - 10\\ - - - - - - - - - - - - - - - \\{5^1} + {1^5} + {0^5} = 5 + 1 + 0 = 6\end{array}\)

\(\begin{array}{l}{\left( {3 + 2} \right)^2} = {2^2} + {3^2}\\\\\left\{ \begin{array}{l}{\left( {3 + 2} \right)^2} = {5^2} = 25\\\\{2^2} + {3^2} = 4 + 9 = 13\end{array} \right.\\\\ \Rightarrow {\left( {3 + 2} \right)^2} \ne {2^2} + {3^2}\end{array}\)

نادرست است.

\(\begin{array}{l}{\left( {4 \times 3} \right)^2} = {3^2} \times {4^2}\\\\\left\{ \begin{array}{l}{\left( {4 \times 3} \right)^2} = {12^2} = 144\\\\{3^2} \times {4^2} = 9 \times 16 = 144\end{array} \right.\\\\ \Rightarrow {\left( {4 \times 3} \right)^2} = {3^2} \times {4^2}\end{array}\)

درست می باشد.

\(\begin{array}{l}{\left( {\frac{2}{3}} \right)^2} = \frac{{22}}{{32}}\\\\\left\{ \begin{array}{l}{\left( {\frac{2}{3}} \right)^2} = \frac{2}{3} \times \frac{2}{3} = \frac{4}{9}\\\\\frac{{22}}{{32}} = \frac{{11}}{{16}}\end{array} \right.\\\\ \Rightarrow {\left( {\frac{2}{3}} \right)^2} \ne \frac{{22}}{{32}}\end{array}\)

نادرست است.

\(\begin{array}{l}5 \times {6^2} = {\left( {6 \times 5} \right)^2}\\\\5 \times {6^2} = 5 \times 36 = 180\\\\{\left( {6 \times 5} \right)^2} = {30^2} = 900\\\\ \Rightarrow 5 \times {6^2} \ne {\left( {6 \times 5} \right)^2}\end{array}\)

نادرست است.

\(\begin{array}{l}{2^2} \times {5^2} = {10^2}\\\\\left\{ \begin{array}{l}{2^2} \times {5^2} = 4 \times 25 = 100\\\\{10^2} = 100\end{array} \right.\\\\ \Rightarrow {2^2} \times {5^2} = {10^2}\end{array}\)

درست می باشد.

\(\begin{array}{l}{2^3} \times {2^4} = {2^7}\\\\\left\{ \begin{array}{l}{2^3} \times {2^4} = 8 \times 16 = 128\\\\{2^7} = 128\end{array} \right.\\\\ \Rightarrow {2^3} \times {2^4} = {2^7}\end{array}\)

درست می باشد.

ابتدا هر عدد را از حالت توان به ضرب تبدیل می کنیم، سپس هر کدام را محاسبه می کنیم و در نهایت با هم جمع می زنیم و حاصل را بدست می آوریم:

\(\begin{array}{l}{2^8} + {8^2} = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 + 8 \times 8\\\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 256 + 64 = 320\end{array}\)