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

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

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

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

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

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

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

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:

\(\frac{1}{6}-\left(-\frac{10}{3}\right)=\frac{1}{6}+\frac{10}{3}=\frac{7}{2}\)

bố mầy đéo hiểu cái éo gì

12fgergtefe

Gợi ý :  Phân tích hết ra thành tích các thừa số nguyên tố rồi đặt cái chung ra ngoài

-> rút gọn

-> kết quả

P/S : bài này cx ko dài lắm nhưg lười  ^^

ko được nói tục

Ta có \(A=\frac{2^{12}.3^5-\left(2^2\right)^6.\left(3^2\right)^2}{2^{12}.3^6+\left(2^3\right)^4.3^5}-\frac{5^{10}.7^3-\left(5^2\right)^5.\left(7^2\right)^2}{\left(5^3\right)^3.7^3+5^9.7^3.2^3}\)

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

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

\(=\frac{2}{12}-\frac{5\left(-6\right)}{9}\)\(=\frac{1}{6}+\frac{30}{9}=\frac{7}{2}\)

Vậy A=7/2

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

    = \(\frac{2^{12}.3^4\left(3-1\right)}{2^{12}.3^5\left(3+1\right)}-\frac{5^{10}.7^3.\left(1-7\right)}{5^9.7^3.\left(1+2^3\right)}\) = \(\frac{2}{3.4}-\frac{5.\left(-6\right)}{9}\)= \(\frac{1}{6}-\frac{-10}{3}\)= 1/6 + 10/3 = 7/2

7/2 la dung

\(A=\frac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6-2^{12}.3^5}-\frac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3-5^9.7^6}\)

\(=\frac{2^{12}.3^4\left(3-1\right)}{2^{12}.3^5\left(3+1\right)}-\frac{5^{10}.7^3.\left(1-7\right)}{5^9.7^3.\left(1+2^3\right)}=\frac{2}{3.4}-\frac{5.\left(-6\right)}{9}=\frac{1}{6}-\frac{-10}{3}=\frac{1}{6}+\frac{10}{3}=\frac{7}{2}\)

Bài 2: 

a) Ta có: \(f\left(2\right)-f\left(-1\right)=7\)

\(\Leftrightarrow2\left(m-1\right)-\left(-1\right)\cdot\left(m-1\right)=7\)

\(\Leftrightarrow2m-2+m-1=7\)

\(\Leftrightarrow3m-3=7\)

\(\Leftrightarrow3m=10\)

hay \(m=\dfrac{10}{3}\)

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

= \(\dfrac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}-\dfrac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3+5^9.14^3}\)

= \(\dfrac{2^{12}\left(3^5-3^4\right)}{2^{12}\left(3^6+3^5\right)}-\dfrac{5^{10}\left(7^3-7^4\right)}{5^9\left(7^3+14^3\right)}\)

=\(\dfrac{3^5-3^4}{3^6+3^5}-\dfrac{5\left(7^3-7^4\right)}{7^3+14^3}\)

=\(\dfrac{243-81}{729+243}-\dfrac{5\left(343-2401\right)}{343+2744}\)

=\(\dfrac{162}{972}-\dfrac{5\left(-2058\right)}{3087}\)

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

= \(\dfrac{1}{6}+\dfrac{20}{6}\)

=\(\dfrac{21}{6}=3,5\)