B=5^2*6^11*16^2+6^2*12^6*15^2/2*6^12*10^4-81^2*960^3
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\(=\dfrac{5^2\cdot6^{11}\cdot2^8+6^2\cdot6^6\cdot2^6\cdot3^2\cdot5^2}{2\cdot6^{12}\cdot10^4-3^8\cdot2^{18}\cdot3^3\cdot5^3}\)
\(=\dfrac{5^2\cdot3^{11}\cdot2^{19}+2^8\cdot2^6\cdot3^8\cdot3^2\cdot5^2}{2^{13}\cdot3^{12}\cdot5^4\cdot2^4-3^{11}\cdot2^{18}\cdot5^3}\)
\(=\dfrac{5^2\cdot3^{11}\cdot2^{19}+2^{14}\cdot3^{10}\cdot5^2}{2^{17}\cdot3^{12}\cdot5^4-3^{11}\cdot2^{18}\cdot5^3}\)
\(=\dfrac{5^2\cdot3^{10}\cdot2^{14}\left(3\cdot2^5+1\right)}{2^{17}\cdot3^{11}\cdot5^3\left(3\cdot5-2\right)}\)
\(=\dfrac{1}{5}\cdot\dfrac{1}{3}\cdot\dfrac{1}{8}\cdot\dfrac{96+1}{13}=\dfrac{97}{5\cdot3\cdot8\cdot13}\)
\(\frac{5^2.6^{11}.16^2+6^2.12^6.15^2}{2.6^{12}.10^4-81^2.960^3}\)
\(=\frac{2^{19}.5^2.3^{11}+2^{14}.3^{10}.5^2}{2^{17}.3^{12}.5^4-2^{18}.3^{11}.5^3}\)
\(=\frac{2^{14}.3^{10}.5^2\left(2^5.3+1\right)}{2^{17}.3^{11}.5^3\left(3.5-2\right)}=\frac{97}{2^3.3.5.13}=\frac{97}{1560}\)
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