\(\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}.12^{10}}\)
\(=\frac{4^9.2.9^3.3^3+3.5.4^9.9^3.3^2}{6^9.2^{10}.2^{10}.6^{10}}\)
\(=\frac{4^9.9^3.3^2.6+4^9.9^3.3^2.15}{6^{19}.2^{20}}\)
\(=\frac{4^9.9^3.3^2.31}{2^{39}.3^{19}}\)
\(=\frac{4^9.3^6.31}{4^{19}.2.3^{17}}\)
\(=\frac{31}{4^{10}.3^{11}.2}\)