\(\dfrac{5^2\cdot6\cdot\left(-16\right)^2+6^2\left(-12\right)^6\left(-15\right)^2}{2\left(-6\right)\cdot2\cdot10^4-81^2\cdot960^3}=\dfrac{3\cdot5^2\cdot2^9+2^{14}\cdot3^{10}\cdot5^2}{-2^7\cdot3\cdot5^4-2^{18}\cdot3^{11}\cdot5^3}=\dfrac{2^9\cdot3\cdot5^2\left(1+2^5\cdot3^9\right)}{-2^7\cdot3\cdot5^3\left(5+2^{11}\cdot3^{10}\right)}=-\dfrac{2^2\left(1+2^5\cdot3^9\right)}{5\left(5+2^{11}\cdot3^{10}\right)}\)

Đề tự chế???

\(\dfrac{5^2.6\left(-16\right)^2+6^2\left(-12\right)^6\left(-15^6\right)}{2\left(-6\right).2.10^4-81^2.960^3}=\dfrac{3.5^2.2^9+2^{18}.3^{11}.5^3}{-2^7.3.5^4-2^{18}.3^{11}.5^3}\)

=\(\dfrac{2^9.3.5^2\left(1+2^2.3^9\right)}{-2^7.3.5^3\left(5+2^{11}.3^{10}\right)}=\dfrac{2^2\left(1+2^5.3^9\right)}{-5\left(5+2^{11}.3^{10}\right)}\)

\(=\dfrac{4\left(1+1\right)}{-5\left(5+2^6.3\right)}=\dfrac{8}{-985}\)

ai làm nhanh mình tick cho

\(=\dfrac{5^2\cdot6^{11}\cdot2^8+6^2\cdot6^6\cdot2^6\cdot15^2}{2\cdot6^{12}\cdot10^4-3^8\cdot2^{18}\cdot3^3\cdot5^3}\)

\(=\dfrac{5^2\cdot2^{19}\cdot3^{11}+3^8\cdot2^8\cdot2^6\cdot3^2\cdot5^2}{2^{13}\cdot3^{12}\cdot2^4\cdot5^4-3^{11}\cdot2^{18}\cdot5^3}\)

\(=\dfrac{5^2\cdot2^{19}\cdot3^{11}+3^{10}\cdot2^{14}\cdot5^2}{2^{17}\cdot3^{12}\cdot5^4-3^{11}\cdot2^{18}\cdot5^3}\)

\(=\dfrac{5^2\cdot2^{14}\cdot3^{10}\left(2^5\cdot3+1\right)}{2^{17}\cdot3^{11}\cdot5^3\left(3\cdot5-2\right)}\)

\(=\dfrac{1}{5}\cdot\dfrac{1}{8}\cdot\dfrac{1}{3}\cdot\dfrac{32\cdot3+1}{15-2}\)

\(=\dfrac{1}{120}\cdot\dfrac{97}{13}=\dfrac{97}{1560}\)

?

???

a: \(A=\dfrac{5^2\cdot3^{11}\cdot2^{11}\cdot2^8+3^2\cdot2^2\cdot2^{12}\cdot3^6\cdot3^2\cdot5^2}{2\cdot2^{12}\cdot3^{12}\cdot2^4\cdot5^4-3^8\cdot960^3}\)

\(=\dfrac{5^2\cdot3^{11}\cdot2^{19}+3^{10}\cdot2^{14}\cdot5^2}{2^{17}\cdot3^{12}\cdot5^4-3^{11}\cdot2^{18}\cdot5^3}\)

\(=\dfrac{5^2\cdot2^{14}\cdot3^{10}\left(3\cdot2^5+1\right)}{2^{17}\cdot3^{11}\cdot5^3\left(3\cdot5-2\right)}=\dfrac{1}{5}\cdot\dfrac{1}{8}\cdot\dfrac{1}{10}\cdot\dfrac{97}{13}=\dfrac{97}{5200}\)

b: \(B=\dfrac{2^{12}\cdot3^{10}+2^9\cdot3^9\cdot2^3\cdot3\cdot5}{2^{12}\cdot3^{12}-2^{11}\cdot3^{11}}\)

\(=\dfrac{2^{12}\cdot3^{10}\cdot\left(1+5\right)}{2^{11}\cdot3^{11}\left(2\cdot3-1\right)}=\dfrac{2}{3}\cdot\dfrac{6}{5}=\dfrac{12}{15}=\dfrac{4}{5}\)

Ta có: \(B=\frac{5^2.6^{11}.16^2+6^2.12^6.15^2}{2.6^{12}.10^4-81^2.960^3}=\frac{5^2.\left(2.3\right)^{11}.\left(4^2\right)^2+\left(2.3\right)^2.\left(2^2.3\right)^6.\left(3.5\right)^2}{2.\left(2.3\right)^{12}.\left(2.5\right)^4-\left(3^4\right)^2.\left(2^6.3.5\right)^3}\)

\(\frac{5^2.2^{11}.3^{11}.2^8+2^2.3^2.2^{12}.3^6.3^2.5^2}{2.2^{12}.3^{12}.2^4.5^4-3^8.2^{18}.3^3.5^3}=\frac{5^2.2^{19}.3^{11}+2^{14}.3^{10}.5^2}{2^{17}.3^{12}.5^4-3^{11}.2^{18}.5^3}\)

\(=\frac{5^2.2^{14}.3^{10}.\left(2^5.3+1\right)}{2^{17}.3^{11}.5^3.\left(3.5-2\right)}=\frac{2^{14}.3^{10}.5^2.97}{2^{17}.3^{11}.5^3.13}=\frac{1.1.1.97}{2^3.3.5.13}=\frac{97}{1560}\)

\(B=\frac{5^2.6^{11}.16^2+6^2.12^6.15^2}{2.6^{12}.10^4-81^2.960^3}\)

\(B=\frac{5^2.2^{11}.3^{11}.2^{4^2}+2^2.3^2.2^{2^6}.3^6.3^2.5^2}{2.2^{12}.3^{12}.10^4-3^{4^2}.2^{5^3}.3^3}\)

\(B=\frac{5^2.2^{11}.2^8.3^{11}+2^2.2^{12}.3^2.3^6.3^2.5^2}{2^{13}.3^{12}.10^4-3^8.3^3.2^{15}}\)

\(B=\frac{5^2.2^{19}.3^{11}+2^{14}.3^{10}.5^2}{2^{13}.3^{12}.10^4-3^{11}.2^{15}}\)

\(B=\frac{5^2.2^{14}.3^{10}.\left(2^5.3+1\right)}{2^{13}.3^{11}.\left(3.10^4-2^2\right)}\)

\(B=\frac{5^2.2^{14}.3^{10}.97}{2^{13}.3^{11}.29996}\)

\(B=\frac{5^2.2.97}{3.29996}\)

\(B=\frac{4850}{89988}\)

\(B=\frac{2425}{44994}\)

leminhduc giải sai rồi

Mình nhìn vào cách làm đã biết rồi

Kết quả không đúng đâu

http://olm.vn/hoi-dap/question/425436.html

\(\frac{5^2.6^{11}.16^2+6^2.12^6.15^2}{2.6^{12}.10^4-81^2.960^3}=\frac{5^2.6^{11}.6^2.6^2.6^6.2^6.3^2.5^2}{2.2^{12}.3^{12}2^4.5^4-3^8.2^{15}.3^3}=\frac{5^6.6^{21}.2^8.3^2}{2^{17}.3^{12}.5^4-3^{11}.2^{15}}=\frac{5^6.3^{23}.2^{29}}{3^{11}.2^{15}.\left(2^2.3.5^4-1\right)}=\frac{5^6.3^{13}.2^{14}}{2^2.3.5^4-1}\)

Ta có:

\(\frac{5^2.6^{11}.16^6.12^6.15^2}{2.6^{12}.10^4-81^2.960^3}\Leftrightarrow\frac{5^2.6^{11}.16^6.12^2.15^2}{2.6^{11}.6.10^4-81^2.960^3}\)

\(\Leftrightarrow\frac{5^2.16^6.12^2.15}{2.6.10^4-81^2.960^3}\Leftrightarrow\frac{5^2.16^2.12.12.15}{\left(2.6\right).10^4-81^2.960^3}\)

\(\Leftrightarrow\frac{5^2.16^2.12.12.15}{12.10^4-81^2.960^3}\Leftrightarrow\frac{5^2.16^2.12.15}{10^4-81^2.960}\)
\(\Leftrightarrow\frac{5^2.16^2.12.3.5}{10^4-3^8.960}\Leftrightarrow\frac{5^2.16^2.12.3.5}{10^4-3^7.3.960}\Leftrightarrow\frac{5^2.16^2.12.5}{10^4-3^7.960}\)

Ps: Không chắc chắn đúng! Thầy cũng cho mình làm bài này hôm nay. Mình cũng làm cách tương tự như trên nhưng chưa biết đúng hay sai! Bạn thông cảm

làm cách trình bày ra nhé biết  kết quả là \(\frac{388}{7199}\)

em cũng chịu thôi khó quá 

Ta có: \(\frac{5^2.6^{11}.16^2+6^2.12^6.15^2}{2.6^{12}.10^4-81^2.960^3}\)

\(=\frac{5^2.2^{11}.3^{11}.2^8+2^2.3^2.3^6.2^{12}.5^2.3^5}{2.2^{12}.3^{12}.2^4.5^4-3^8.2^{18}.3^3.5^3}\)

\(=\frac{5^2.2^{19}.3^{11}+3^{13}.2^{14}.5^2}{2^{17}.3^{12}.5^4-2^{18}.3^{11}.5^3}\)

\(=\frac{\left(5^2.2^{14}.3^{11}\right)\left(2^5+3^2\right)}{\left(2^{17}.3^{11}.5^3\right)\left(3.5-2\right)}\)

\(=\frac{\left(2^5+3^2\right)}{\left(2^3.5\right)\left(3.5-2\right)}\)

\(=\frac{32+9}{40.13}\)

\(=\frac{41}{520}\)

\(\frac{5^2.6^{11}.16^2+6^2.12^6.15^2}{2.6^{12}.10^4-81^2.960^3}\)

= \(\frac{5^2.3^{11}.2^{11}.2^8-2^2.3^2.3^6.2^{12}.3^2.5^2}{2.2^{12}.3^{12}.2^4.5^4-3^8.\left(2^6.3.5\right)^3}\)

= \(\frac{5^2.3^{11}.2^{19}-2^{14}.3^{10}.5^2}{2^{17}.3^{12}.5^4-3^8.2^{18}.3^3.5^3}\)

= \(\frac{5^2.3^{10}.2^{14}.\left(3.2^5-1\right)}{2^{17}.3^{12}.5^4-3^{11}.2^{18}.5^3}\)

= \(\frac{5^2.3^{10}.2^{14}.95}{2^{17}.3^{11}.5^3.\left(3.5-2\right)}\)

= \(\frac{5^2.3^{10}.2^{14}.5.19}{2^{17}.3^{11}.5^3.13}\)

= \(\frac{19}{2^3.13}=\frac{19}{104}\)