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=> A=\(\)\(\frac{5^2.6^9.10+6^5.2^3.15^3}{5^2.6^8.10-2.6^8.10^3}=\frac{5^2.6^9.2.5+6^5.2^3.\left(3.5\right)^3}{5^2.6^8.2.5-2.6^8.\left(2.5\right)^3}\)

\(\Rightarrow A=\frac{5^3.6^9.2+6^5.2^3.3^3.5^3}{5^3.6^8.2-2.6^8.2^3.5^3}=\frac{5^3.6^9.2+\left(2.3\right)^3.5^3}{5^3.6^8.2-2^4.6^8.5^3}\)

\(\Rightarrow A=\frac{5^3.6^8.6.2+6^8.5^3}{5^3.6^8.2-2^4.6^8.5^3}=\frac{5^3.6^8.\left(6.2+1\right)}{5^3.6^8.\left(2-2^4\right)}\)

\(\Rightarrow A=\frac{6.2+1}{2-2^4}=\frac{12+1}{-14}=\frac{13}{-14}\)

\(=\dfrac{5^2\cdot2^9\cdot3^9\cdot2\cdot5+2^5\cdot2^3\cdot3^5\cdot5^3\cdot3^3}{5^2\cdot2^8\cdot3^8\cdot2\cdot5-2\cdot2^8\cdot3^8\cdot2^3\cdot5^3}\)

\(=\dfrac{5^3\cdot2^{10}\cdot3^9+5^3\cdot2^8\cdot3^8}{5^3\cdot2^9\cdot3^8-5^3\cdot2^{12}\cdot3^8}\)

\(=\dfrac{5^3\cdot2^8\cdot3^8\left(2^2\cdot3+1\right)}{5^3\cdot2^9\cdot3^8\left(1-2^3\cdot1\right)}=\dfrac{1}{2}\cdot\dfrac{13}{1-9}=-\dfrac{13}{16}\)

Có: \(\dfrac{5^2.6^9.10+6^5.2^3.15^3}{5^2.6^8.10-2.6^8.10}=\dfrac{5^2.2^9.3^9.2.5+2^5.3^5.2^3.3^3.5^3}{5^2.2^8.3^8.2.5-2.2^8.3^8.2^3.5^3}\)

=\(\dfrac{2^{10}.3^95^3+2^8.3^8.5^3}{2^9.3^8.5^3-2^{12}.3^8.5^3}=\dfrac{2^8.3^8.5^3.\left(12+1\right)}{2^8.3^8.5^3\left(2-16\right)}\)

= \(\dfrac{12+1}{2-16}=\dfrac{-13}{14}\)

\(\frac{5^2.6^9.10+6^5.2^3.15^3}{5^2.6^8.10-2.6^8.10^3}=\frac{5^2.2^9.3^9.2.5+2^5.3^5.2^3.5^3.3^3}{5^2.2^8.3^8.2.5-2.2^8.3^8.2^3.5^3}\)

\(=\frac{2^{10}.3^9.5^3+2^8.3^8.5^3}{2^9.3^8.5^3-2^{12}.3^8.5^3}=\frac{2^8.3^8.5^3\left(2^2.3+1\right)}{2^9.3^8.5^3\left(1-2^3\right)}\)

\(=\frac{13}{2.-7}=-\frac{13}{14}\)

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

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

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

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

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

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

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

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

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

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

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

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

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