\(\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}=\frac{2^{19}.\left(3^3\right)^3+3.5.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{10}+\left(2^2.3\right)^{10}}\)
\(=\frac{2^{19}.3^9+3.5.2^{18}.3^8}{2^9.3^9.2^{10}+2^{20}.3^{10}}\)
\(=\frac{2^{18}.3^8.\left(2.3+3.5\right)}{2^{18}.3^9.\left(2+2^2.3\right)}\)
\(=\frac{6+15}{3.\left(2+12\right)}\)
\(=\frac{21}{3.14}=\frac{21}{42}=\frac{1}{2}\)
\(A=\frac{2^{19}\cdot3^9+3\cdot5\cdot2^{18}\cdot3^8}{2^9\cdot3^9\cdot2^{10}+4^{10}\cdot3^{10}}=\frac{2^{18}\cdot3^9\times\left(2+5\right)}{2^{19}\cdot3^9\times\left(1+6\right)}=\frac{1}{2}\)
