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\(A=\dfrac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\dfrac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)
\(=\dfrac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}-\dfrac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3+5^9.2^3.7^3}\)
\(=\dfrac{2^{12}.3^4.\left(3-1\right)}{2^{12}.3^5.\left(3+1\right)}-\dfrac{5^{10}.7^3.\left(1-7\right)}{5^9.7^3.\left(1+2^3\right)}\)
\(=\dfrac{2^{12}.3^4.2}{2^{12}.3^5.4}-\dfrac{5^{10}.7^3.\left(-6\right)}{5^9.7^3.9}\)
\(=\dfrac{1}{6}-\dfrac{-10}{3}\)
\(=\dfrac{7}{2}\)
\(A=\dfrac{2^{12}\cdot3^5-2^{12}\cdot3^4}{2^{12}\cdot3^6+2^{12}\cdot3^5}-\dfrac{5^{10}\cdot7^3-5^{10}\cdot7^4}{5^9\cdot7^3+5^9\cdot7^3\cdot2^3}\)
\(=\dfrac{3^4\left(3-1\right)}{3^5\left(3+1\right)}-\dfrac{5^{10}\cdot7^3\left(1-7\right)}{5^9\cdot7^3\cdot9}\)
\(=\dfrac{1}{3\cdot2}-\dfrac{1}{5}\cdot\dfrac{-6}{9}=\dfrac{1}{6}+\dfrac{6}{45}=\dfrac{45+36}{270}=\dfrac{81}{270}=\dfrac{3}{10}\)
\(\dfrac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\dfrac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)
\(=\dfrac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}-\dfrac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3+5^9.7^3.2^3}\)
\(=\dfrac{2^{12}(3^5-3^4)}{2^{12}(3^6+3^5)}-\dfrac{5^{10}(7^3-7^4)}{5^9.7^3(1+2^3)}\)
\(=\dfrac{2^{12}.162}{2^{12}.972}-\dfrac{5^{10}(-2058)}{5^9.7^3.9}\)
\(=\dfrac{2^{12}.162}{2^{12}.972}-\dfrac{5^{10}(-2058)}{5^9.7^3.9}\)
\(=\dfrac{162}{972}-\dfrac{5(-2058)}{7^3.9}\)
\(=\dfrac{2.3^4}{2^2.3^5}-\dfrac{5.2.7^3.\left(-3\right)}{7^3.3^2}\)
\(=\dfrac{1}{2.3}-\left(\dfrac{-\left(5.2\right)}{3}\right)\)
\(=\dfrac{1}{6}-\left(\dfrac{-10}{3}\right)\)
\(=\dfrac{7}{2}\)
\(A=\frac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^{^6}+8^4.3^5}-\frac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^{^3}+5^9.12^3}\)
\(A=\frac{1}{6}-\frac{-10}{3}\)
\(A=\frac{7}{2}\)
\(\frac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\frac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)
Phân tích từ số:
\(\frac{2^{12}.3^5-4^2.4^4.3^4}{2^{12}.3.3^5+4^2.4^4.3.3^4}=\frac{1}{6}\)
\(\frac{5^9.5.7^3-5^9.5.7^3.7}{5^9.7^3+5^9.2^3.7^3}=\frac{-10}{3}\)
Sau khi rút gọn là:
\(\frac{1}{6}-\left(-\frac{10}{3}\right)=\frac{1}{6}+\frac{10}{3}=\frac{7}{2}\)
\(B=\frac{1-\frac{1}{\sqrt{49}}+\frac{1}{49}-\frac{1}{\left(7\sqrt{7}\right)^2}}{\frac{\sqrt{64}}{2}-\frac{4}{7}+\frac{2^2}{7^2}-\frac{4}{343}}\)
\(B=\frac{1-\frac{1}{7}+\frac{1}{49}-\frac{1}{343}}{\frac{8}{2}-\frac{4}{7}+\frac{4}{49}-\frac{4}{343}}\)
\(B=\frac{\frac{343}{343}-\frac{49}{343}+\frac{7}{343}-\frac{1}{343}}{4-\frac{4}{7}+\frac{28}{343}-\frac{4}{343}}\)
\(B=\frac{\frac{300}{343}}{\frac{28}{7}-\frac{4}{7}+\frac{24}{343}}\)
\(B=\frac{\frac{300}{343}}{\frac{24}{7}+\frac{24}{343}}\)
\(B=\frac{\frac{300}{343}}{\frac{1323}{343}+\frac{24}{343}}\)
\(B=\frac{300}{343}:\frac{1347}{343}\)
\(B=\frac{100}{449}\)
\(A=\frac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\frac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)
\(A=\frac{2^{12}.3^5-2^{12}.3^6}{2^{12}.3^6+2^{12}.3^5}-\frac{5^{10}.7^3-5^{10}.7^6}{5^9.7^3+5^9.2^3.7^3}\)
\(A=\frac{2^{12}.3^5\left(1-3\right)}{2^{12}.3^5.\left(3+1\right)}-\frac{5^{10}.7^3.\left(1-7^3\right)}{5^9.7^3.\left(1+8\right)}\)
\(A=\frac{-2}{4}-\frac{5.\left(-342\right)}{9}\)
\(A=\frac{-1}{2}+\frac{1710}{9}\)
\(A=\frac{-1}{2}+190\)
\(A=\frac{-1}{2}+\frac{380}{2}\)
\(A=\frac{379}{2}\)
\(A=\dfrac{2^{15}.3^5-4^6.9^2}{\left(2^2.3\right)+8^4.3^5}-\dfrac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)
\(\Leftrightarrow A=\dfrac{2^{15}.3^5-\left(2^2\right)^6.\left(3^2\right)^2}{2^2.3+\left(2^3\right)^4.3^5}-\dfrac{5^{10}.7^3-\left(5^2\right)^5.\left(7^2\right)^2}{\left(5^3\right)^3.7^3+5^9.14^3}\)
\(\Leftrightarrow A=\dfrac{2^{15}.3^5-2^{12}.3^4}{2^2.3+2^{12}.3^5}-\dfrac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3+5^9.\left(7.2\right)^3}\)
\(\Leftrightarrow A=\dfrac{2^{12}.3^4\left(2^3.3-1\right)}{2^2.3\left(1+2^{10}.3^4\right)}-\dfrac{5^{10}.7^3\left(1-7\right)}{5^9.7^3\left(1+2^3\right)}\)
\(\Leftrightarrow A=\dfrac{2^{10}.3^3\left(2^3.3-1\right)}{\left(1+2^{10}.3^4\right)}-\dfrac{5\left(1-7\right)}{\left(1+2^3\right)}\)
\(\Leftrightarrow A=\dfrac{1024.9\left(8.3-1\right)}{\left(1+1024.81\right)}-\dfrac{5\left(1-7\right)}{\left(1+8\right)}\)
\(\Leftrightarrow A=\dfrac{9216\left(24-1\right)}{\left(1+82944\right)}-\dfrac{5\left(1-7\right)}{\left(1+8\right)}\)
\(\Leftrightarrow A=\dfrac{9216.23}{82945}-\dfrac{5\left(-6\right)}{9}\)
\(\Leftrightarrow A=\dfrac{211968}{82945}+\dfrac{30}{9}\)
\(\Leftrightarrow A=\dfrac{1907712}{746505}+\dfrac{2488350}{746505}\)
\(\Leftrightarrow A=\dfrac{1907712+2488350}{746505}\)
\(\Leftrightarrow A=\dfrac{4396062}{746505}\)
Đề đúng: Kết quả phép tính \(\dfrac{2^{12}\times3^5-4^6\times9^2}{\left(2^2\times3\right)^6+8^4\times3^5}-\dfrac{5^{10}\times7^3-25^5\times49^2}{\left(125\times7\right)^3+5^9\times14^3}\) là ...
Giải:
Ta có:
\(\dfrac{2^{12}\times3^5-4^6\times9^2}{\left(2^2\times3\right)^6+8^4\times3^5}-\dfrac{5^{10}\times7^3-25^5\times49^2}{\left(125\times7\right)^3+5^9\times14^3}\) \(=\dfrac{2^{12}\times3^5-\left(2^2\right)^6\times\left(3^2\right)^2}{\left(2^2\right)^6\times3^6+\left(2^3\right)^4\times3^5}-\dfrac{5^{10}\times7^3-\left(5^2\right)^5\times\left(7^2\right)^2}{\left(5^3\times7\right)^3+5^9\times\left(2\times7\right)^3}\) \(=\dfrac{2^{12}\times3^5-2^{12}\times3^4}{2^{12}\times3^6+2^{12}\times3^5}-\dfrac{5^{10}\times7^3-5^{10}\times7^4}{\left(5^3\right)^3\times7^3+5^9\times2^3\times7^3}\) \(=\dfrac{2^{12}\times3^4\times\left(3-1\right)}{2^{12}\times3^5\times\left(3+1\right)}-\dfrac{5^{10}\times7^3\times\left(1-7\right)}{5^9\times7^3+5^9\times2^3\times7^3}\) \(=\dfrac{2^{12}\times3^4\times2}{2^{12}\times3^5\times4}-\dfrac{5^{10}\times7^3\times\left(-6\right)}{5^9\times7^3\times\left(1+2^3\right)}\) \(=\dfrac{2^{13}\times3^4}{2^{12}\times3^5\times2^2}-\dfrac{5^{10}\times7^3\times\left(-6\right)}{5^9\times7^3\times\left(1+8\right)}\) \(=\dfrac{2^{13}\times3^4}{2^{14}\times3^5}-\dfrac{5^{10}\times7^3\times\left(-6\right)}{5^9\times7^3\times9}\) \(=\dfrac{1}{6}-\dfrac{-10}{3}\) \(=\dfrac{7}{2}\)
Vậy kết quả của phép tính đã cho là \(\dfrac{7}{2}\).
\(\dfrac{2^{12}\cdot3^5-4^6\cdot9^2}{\left(2^2\cdot3\right)^6+8^4\cdot3^5}-\dfrac{5^{10}\cdot7^3-25^5\cdot49^2}{\left(125\cdot7\right)^3+5^9\cdot14^3}\)
\(=\dfrac{2^{12}\cdot3^5-\left(2^2\right)^6\cdot\left(3^2\right)^2}{\left(2^2\right)^6\cdot3^6+\left(2^3\right)^4\cdot3^5}-\dfrac{5^{10}\cdot7^3-\left(5^2\right)^5\cdot\left(7^2\right)^2}{\left(5^3\cdot7\right)^3+5^9\cdot\left(2\cdot7\right)^3}\)
\(=\dfrac{2^{12}\cdot3^5-2^{12}\cdot3^4}{2^{12}\cdot3^6+2^{12}\cdot3^5}-\dfrac{5^{10}\cdot7^3-5^{10}\cdot7^4}{5^9\cdot7^3+5^9\cdot2^3\cdot7^3}\)
\(=\dfrac{2^{12}\cdot3^4\left(3-1\right)}{2^{12}\cdot3^5\left(3+1\right)}-\dfrac{5^{10}\cdot7^3\left(1-7\right)}{5^9\cdot7^3\left(1+2^3\right)}\)
\(=\dfrac{2}{3\cdot4}-\dfrac{5\cdot\left(1-7\right)}{1+8}\)\(=\dfrac{1}{3\cdot2}-\dfrac{5\cdot\left(-6\right)}{9}\)
\(=\dfrac{1}{6}-\dfrac{-10}{3}=\dfrac{1}{6}+\dfrac{10}{3}=\dfrac{7}{2}\)