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

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 \(\frac{388}{7199}\)

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câu hỏi tương tự nha bạn

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

\(A=\frac{\left(5^2.2^{11}.3^{11}.2^8+2^2.3^2.3^3.2^{12}.3^2.5^2\right).10}{2.2^{12}.3^{12}.2^4.5^4-9^4.2^{18}.3^3.5^3}\)

\(A=\frac{5^2.2^{11}.3^{11}.2^8.2.5+2^2.3^2.2^{12}.3^25^2.2.5}{2^{15}.\left(2^2.3^{12}.5^4-9^4.2^3.3^3.5^3\right)}\)

\(A=\frac{2^{15}\left(5^3.2^5.3^{11}+3^4.5^3\right)}{2^{15}.\left(2^2.3^{12}.5^4-9^4.2^3.3^3.5^3\right)}\)

\(A=\frac{5^3.2^5.3^{11}+3^4.5^3}{2^2.3^{12}.5^4-9^4.2^3.3^3.5^3}\)

\(A=\frac{5^3\left(2^5.3^{11}+3^4\right)}{5^3\left(2^2.3^{12}.5-9^4.2^3.3^3\right)}\)\(A=\frac{2^5.3^{11}+3^4}{2^2.3^{12}.5-9^4.2^3.3^3}\)

\(A=\frac{3^4.\left(2^5.3^8.5+1\right)}{3^4\left(2^2.3^8.5-3^4.2^3.3^3\right)}\)

\(A=\frac{2^5.3^8.5+1}{2^2.3^8.5-3^4.2^3.3^3}\)

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