\(\dfrac{5.14^{15}.9^9-4.3^{20}.8^9}{5.2^9-7.2^{29}.27^6}\)
\(=\dfrac{5.2^{30}.3^{18}-2^2.2^{27}.3^{20}}{5.2^9.2^{19}.3^{19}-7.2^{29}.3^{18}}\)
\(=\dfrac{2^{29}.3^{18}\left(5.2-3^2\right)}{2^{28}.3^{18}\left(5.3-7.2\right)}=\dfrac{2^{28}.3^{18}.2}{2^{28}.3^{18}}=2\)