\(\dfrac{6^9.\left(-2\right)^{10}+12^{10}}{2^{19}.27^3+15.4^9.9^4}\)\(=\dfrac{2^9.3^9.2^{10}+3^{10}.2^{20}}{2^{19}.3^9+3.5.2^{18}.3^8}\)
\(=\dfrac{2^{19}.3^9+2^{20}.3^{10}}{2^{19}.3^9+3^9.5.2^{18}}=\dfrac{2^{19}.3^9.\left(1+2.3\right)}{2^{18}.3^9.\left(2+5\right)}\)
\(=\dfrac{2.2^{18}.3^9.7}{2^{18}.3^9.7}=2\)