\(\frac{2\cdot6^9-2^5\cdot18^4}{2^6\cdot6^8}=\frac{2^{10}\cdot3^9-2^9\cdot3^8}{2^{14}\cdot3^8}=\frac{2^9\cdot3^8}{2^{14}\cdot3^8}=\frac{1}{2^5}\)

hình như sai....

Nhìn qua thì thấy sai sai nhưng mà nhìn kĩ............nó sai thật! Để sửa lại: 

\(\frac{2\cdot6^9-2^5\cdot18^4}{2^6\cdot6^8}=\frac{2^9\cdot3^8-2^9\cdot3^8}{2^6\cdot6^8}=0\)

Gọi tổng là A ta có:

\(A.2=\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{18.20}\)

\(A.2=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{18}-\frac{1}{20}\)

\(A.2=\frac{1}{2}-\frac{1}{20}\)

\(A=\frac{9}{20}:2=\frac{9}{40}\)

\(\frac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}\)

\(=\frac{\left(2^2\right)^5.\left(3^2\right)^4-2.\left(2.3\right)^9}{2^{10}.3^8+\left(2.3\right)^8.2^2.5}\)

\(=\frac{2^{10}.3^8-2^{10}.3^9}{2^{10}.3^8+2^8.3^8.2^2.5}\)

\(=\frac{2^{10}.3^8.\left(1-3\right)}{2^{10}.3^8.\left(1+5\right)}\)

\(=\frac{-1}{3}\)

Ta có:

\(\frac{4^5\cdot9^4-2\cdot6^9}{2^{10}\cdot3^8+6^8\cdot20}\)

\(=\frac{2^{10}\cdot3^8-2^{10}\cdot3^9}{2^{10}\cdot3^8+2^{10}\cdot3^8\cdot5}\)

\(=\frac{2^{10}\cdot3^8\cdot\left(1-3\right)}{2^{10}\cdot3^8\cdot\left(1+5\right)}\)

\(=-\frac{2}{6}=-\frac{1}{3}\)

\(\frac{4^5\times9^4-2\times6^9}{2^{10}\times3^8+6^8\times20}\)

\(=\frac{2^{10}\times3^8-2^{10}.3^9}{2^{10}\times3^8+2^{10}\times3^8\times5}\)

\(=\frac{2^{10}\times3^8\left(1-3\right)}{2^{10}\times3^8\left(1+5\right)}\)

\(=\frac{-1}{3}\)

=\(\frac{3\times3\times3\times5\times3\times7\times2\times6\times4\times5}{5\times2\times3\times5\times3\times3\times3\times6\times4}=7\)

\(\frac{9x15x21x12x20}{5x6x45x18x4}=\frac{3x3x15x3x7x3x4x5x4}{5x6x15x3x3x3x2x4}=\frac{15x7x3x4}{6x2}=\frac{1260}{12}=105\)

=\(\frac{1}{96}\)​​

Đúng 100 %

\(\frac{1.2.6.4.6.4.5.2}{2.3.6.8.6.2.2.2.8.10}=\frac{1}{96}\)

Gía trị của biểu thức là : \(\frac{1x2x3x2x2x2x2x3x2x2x2x5x2}{2x3x3x2x4x2x3x2x2x2x2x4x2x5x2}\)= \(\frac{1}{48}\)