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1, Đặt \(A=\frac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\)
\(A=\frac{5.2^{30}.3^{18}-2^2.3^{20}.2^{27}}{5.2^9.2^{19}.3^{19}-7.2^{29}.3^{18}}\)\(A=\frac{2^{28}\left(5.2^2.3^{18}-2.3^{20}\right)}{2^{28}\left(5.3^{19}-7.2.3^{18}\right)}\)
\(A=\frac{5.2^2.3^{18}-2.3^{20}}{5.3^{19}-7.2.3^{18}}\)\(A=\frac{3^{18}\left(5.2^2-2.3^2\right)}{3^{18}\left(5.3-7.2\right)}\)
\(A=\frac{5.2^2-2.3^2}{5.3-7.2}\)\(A=2\)
a, \(\frac{5.4^{15}.9^9-4.3^{20}.8^9}{5.9^2.6^{19}-7.2^{29}.27^6}=\frac{5.\left(2^2\right)^{15}.\left(3^2\right)^9-2^2.3^{20}.\left(2^3\right)^9}{5.2^9.\left(2.3\right)^{19}-7.2^{29}.\left(3^3\right)^6}=\frac{5.2^{30}.3^{18}-2^2.3^{20}.2^{27}}{5.2^9.2^{19}.3^{19}-7.2^{29}.3^{18}}\)\(=\frac{5.2.2^{29}.3^{18}-2^{29}.3^2.3^{18}}{5.2^{28}.3.3^{18}-7.2.2^{28}.3^{18}}=\frac{\left(5.2-3^2\right).2^{29}.3^{18}}{\left(5.3-7.2\right).2^{28}.3^{18}}=2\)