شاه کلید نکات
شاه کلید سوال
1 حاصل عبارت های زیر را به صورت یک عدد توان دار بنویسید.
\(\begin{array}{l}{5^3} \times {5^4} = \\\\{\left( { - 2} \right)^4} \times {\left( { - 2} \right)^2} = \\\\{\left( { - 4} \right)^1} \times {\left( { - 4} \right)^5} = \\\\{7^3} \times 7 = \\\\{\left( {\frac{1}{2}} \right)^5} \times 0/{5^2} = \\\\1/{5^4} \times {\left( {\frac{3}{2}} \right)^4} = \end{array}\)
\({5^3} \times {5^4} = {5^{3 + 4}} = {5^7}\)
\({\left( { - 2} \right)^4} \times {\left( { - 2} \right)^2} = {\left( { - 2} \right)^{4 + 2}} = {\left( { - 2} \right)^6}\)
\({\left( { - 4} \right)^1} \times {\left( { - 4} \right)^5} = {\left( { - 4} \right)^{1 + 5}} = {\left( { - 4} \right)^6}\)
\({7^3} \times 7 = {7^3} \times {7^1} = {7^{3 + 1}} = {7^4}\)
\(\begin{array}{l}{\left( {\frac{1}{2}} \right)^5} \times 0/{5^2} = {\left( {\frac{1}{2}} \right)^5} \times {\left( {\frac{1}{2}} \right)^2} = \\\\{\left( {\frac{1}{2}} \right)^{5 + 2}} = {\left( {\frac{1}{2}} \right)^7}\end{array}\)
\(\begin{array}{l}1/{5^4} \times {\left( {\frac{3}{2}} \right)^4} = {\left( {\frac{3}{2}} \right)^4} \times {\left( {\frac{3}{2}} \right)^4} = \\\\{\left( {\frac{3}{2}} \right)^{4 + 4}} = {\left( {\frac{3}{2}} \right)^8}\end{array}\)
2 با باز کردن عبارت تواندار، جواب را ساده تر کنید و محاسبات را مانند نمونه پاسخ دهید.
\({3^4} = {3^2} \times {3^2} = 9 \times 9 = {9^2}\)
\(\begin{array}{l}{2^6} = \\\\{4^4} = \\\\{5^4} = \end{array}\)
\(\begin{array}{l}{2^6} = {2^3} \times {2^3} = 8 \times 8 = {8^2}\\\\{4^4} = {4^2} \times {4^2} = 16 \times 16 = {16^2}\\\\{5^4} = {5^2} \times {5^2} = 25 \times 25 = {25^2}\end{array}\)
3 اگر \({2^{10}} = 1024\) باشد حاصل \({2^{12}}\) را به دست آورید.
\({2^{12}} = {2^2} \times {2^{10}} = 4 \times 1024 = 4096\)
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