\(A=\dfrac{2^{12}.3^5-\left(2^2\right)^6.\left(3^2\right)^2}{\left(2^2\right)^6.3+\left(2^3\right)^4.3^5}-\dfrac{5^{10}+7^3-\left(5^2\right)^5.\left(7^2\right)^2}{(5^3).7^3+5^9.\left(7^2\right)^3}\)

\(A=\dfrac{2^4.1-2.3^3}{1.1+1.1}-\dfrac{5+1-5.1}{1.1+1.7}\)

\(A=\dfrac{2^4-54}{2}-\dfrac{1.1}{2\cdot7}\)

\(A=(2^3-54)-\dfrac{1}{14}\)

\(A=\left(-46\right)-\dfrac{1}{14}\)

\(A=\dfrac{2^{12}\cdot3^5-2^{12}\cdot3^4}{2^{12}\cdot3^6+2^{12}\cdot3^5}-\dfrac{5^{10}\cdot7^3-5^{10}\cdot7^4}{5^9\cdot7^3+5^9\cdot7^3\cdot2^3}\)

\(=\dfrac{3^4\left(3-1\right)}{3^5\left(3+1\right)}-\dfrac{5^{10}\cdot7^3\left(1-7\right)}{5^9\cdot7^3\cdot9}\)

\(=\dfrac{1}{3\cdot2}-\dfrac{1}{5}\cdot\dfrac{-6}{9}=\dfrac{1}{6}+\dfrac{6}{45}=\dfrac{45+36}{270}=\dfrac{81}{270}=\dfrac{3}{10}\)

\(A=\dfrac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\dfrac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)

\(=\dfrac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}-\dfrac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3+5^9.2^3.7^3}\)

\(=\dfrac{2^{12}.3^4.\left(3-1\right)}{2^{12}.3^5.\left(3+1\right)}-\dfrac{5^{10}.7^3.\left(1-7\right)}{5^9.7^3.\left(1+2^3\right)}\)

\(=\dfrac{2^{12}.3^4.2}{2^{12}.3^5.4}-\dfrac{5^{10}.7^3.\left(-6\right)}{5^9.7^3.9}\)

\(=\dfrac{1}{6}-\dfrac{-10}{3}\)

\(=\dfrac{7}{2}\)

\(\dfrac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\dfrac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)

\(=\dfrac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}-\dfrac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3+5^9.7^3.2^3}\)

\(=\dfrac{2^{12}(3^5-3^4)}{2^{12}(3^6+3^5)}-\dfrac{5^{10}(7^3-7^4)}{5^9.7^3(1+2^3)}\)

\(=\dfrac{2^{12}.162}{2^{12}.972}-\dfrac{5^{10}(-2058)}{5^9.7^3.9}\)

\(=\dfrac{2^{12}.162}{2^{12}.972}-\dfrac{5^{10}(-2058)}{5^9.7^3.9}\)

\(=\dfrac{162}{972}-\dfrac{5(-2058)}{7^3.9}\)

\(=\dfrac{2.3^4}{2^2.3^5}-\dfrac{5.2.7^3.\left(-3\right)}{7^3.3^2}\)

\(=\dfrac{1}{2.3}-\left(\dfrac{-\left(5.2\right)}{3}\right)\)

\(=\dfrac{1}{6}-\left(\dfrac{-10}{3}\right)\)

\(=\dfrac{7}{2}\)

\(P=\dfrac{2^{12}\cdot3^5-2^{12}\cdot3^4}{2^{12}\cdot3^6-2^{12}\cdot3^5}-\dfrac{5^{10}\cdot7^3-5^{10}\cdot7^4}{5^9\cdot7^3+5^9\cdot7^3\cdot8}\)

\(=\dfrac{2^{12}\cdot3^4\left(3-1\right)}{2^{12}\cdot3^5\cdot\left(3-1\right)}-\dfrac{5^{10}\cdot7^3\cdot\left(1-7\right)}{5^9\cdot7^3\cdot\left(1+8\right)}\)

\(=\dfrac{1}{3}-\dfrac{5\cdot\left(-6\right)}{9}=\dfrac{3}{9}+\dfrac{30}{9}=\dfrac{33}{9}=\dfrac{11}{3}\)

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 \(\dfrac{7}{2}\).

\(\dfrac{2^{12}\cdot3^5-4^6\cdot9^2}{\left(2^2\cdot3\right)^6+8^4\cdot3^5}-\dfrac{5^{10}\cdot7^3-25^5\cdot49^2}{\left(125\cdot7\right)^3+5^9\cdot14^3}\)

\(=\dfrac{2^{12}\cdot3^5-\left(2^2\right)^6\cdot\left(3^2\right)^2}{\left(2^2\right)^6\cdot3^6+\left(2^3\right)^4\cdot3^5}-\dfrac{5^{10}\cdot7^3-\left(5^2\right)^5\cdot\left(7^2\right)^2}{\left(5^3\cdot7\right)^3+5^9\cdot\left(2\cdot7\right)^3}\)

\(=\dfrac{2^{12}\cdot3^5-2^{12}\cdot3^4}{2^{12}\cdot3^6+2^{12}\cdot3^5}-\dfrac{5^{10}\cdot7^3-5^{10}\cdot7^4}{5^9\cdot7^3+5^9\cdot2^3\cdot7^3}\)

\(=\dfrac{2^{12}\cdot3^4\left(3-1\right)}{2^{12}\cdot3^5\left(3+1\right)}-\dfrac{5^{10}\cdot7^3\left(1-7\right)}{5^9\cdot7^3\left(1+2^3\right)}\)

\(=\dfrac{2}{3\cdot4}-\dfrac{5\cdot\left(1-7\right)}{1+8}\)\(=\dfrac{1}{3\cdot2}-\dfrac{5\cdot\left(-6\right)}{9}\)

\(=\dfrac{1}{6}-\dfrac{-10}{3}=\dfrac{1}{6}+\dfrac{10}{3}=\dfrac{7}{2}\)

\(\dfrac{7}{2}\)

3,5

\(A=\dfrac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\dfrac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)

\(=\dfrac{2^{12}.3^5-\left(2^2\right)^6.\left(3^2\right)^2}{\left(2^2\right)^6.3^6+\left(2^3\right)^4.3^5}-\dfrac{5^{10}.7^3-\left(5^2\right)^5.\left(7^2\right)^2}{\left(5^3\right)^3.7^3+5^9.\left(7.2\right)^3}\)

\(=\dfrac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}-\dfrac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3+5^9.7^3.2^3}\)

\(=\dfrac{2^{12}.\left(3^5-3^4\right)}{2^{12}.\left(3^6+3^5\right)}-\dfrac{5^{10}.7^3.\left(1-7\right)}{5^9.7^3.\left(1+2^3\right)}\)

\(=\dfrac{1}{6}-\left(\dfrac{-10}{3}\right)\)

\(=\dfrac{7}{2}\).