\(\frac{5^2\times6^{11}\times16^2+6^2\times12^6\times15^2}{2\times6^{12}\times10^4-81^2\times960^3}\)
\(=\frac{5^2\times\left(2\times3\right)^{11}\times\left(2^4\right)^2+\left(2\times3\right)^2\times\left(2^2\times3\right)^6\times\left(3\times5\right)^2}{2\times\left(2\times3\right)^{12}\times\left(2\times5\right)^4-\left(3^4\right)^2\times\left(2^6\times3\times5\right)^3}\)
\(=\frac{5^2\times2^{19}\times3^{11}+2^{14}\times3^{10}\times5^3}{2^{17}\times5^4\times3^{12}-3^{11}\times2^{18}\times5^3}\)
\(=\frac{5^2\times3^{10}\times2^{14}\times\left(2^5\times3+5\right)}{2^{17}\times5^3\times3^{11}\times\left(5\times3-2\right)}\)
\(=\frac{2^5\times3+5}{2^3\times5\times3\times12}\)
\(=\frac{32\times3+5}{8\times15\times12}=\frac{96+5}{120\times12}=\frac{101}{1440}\)
