\(\frac{5.4^{15}.9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\)

= 1

đúng không ?

\(=\frac{5.2^{30}.3^{18}-3^{20}.2^2.2^{27}}{5.2^9.2^{19}.3^{19}-7.2^{29}\cdot3^{18}}=\frac{5.2^{30}.3^{18}-3^{20}.2^{29}}{5.2^{28}.3^{19}-7.2^{29}.3^{18}}=\frac{2^{29}.3^{18}\left(5.2-3^2\right)}{2^{28}.3^{18}\left(5.3-7.2\right)}=\frac{2\left(10-9\right)}{\left(15-14\right)}==\frac{2.1}{1}=2\)

5.4¹⁵.9⁹-4.3²⁰.8⁹=5.2³⁰.3¹⁸-2²⁹.3²⁰=2²⁹.3¹⁸.(5.2-3²)=2²⁹.3¹⁸ 

5.2⁹.6¹⁹-7.2²⁹.27⁶=5.2²⁸.3¹⁹-7.2²⁹.3¹⁸=2²⁸.3¹⁸.(5.3-7.2)=2²⁸.3¹⁸

\(=\frac{5\cdot2^{20}\cdot3^{11}+7\cdot2^{29}\cdot3^{18}}{5\cdot2^{30}\cdot3^{18}-2^{29}\cdot3^{20}}=\frac{2^{20}\cdot3^{11}\left(5+7\cdot2^9\cdot3^7\right)}{2^{29}\cdot3^{18}\left(5\cdot2-3^2\right)}=\frac{5+7\cdot2^9\cdot3^7}{2^9\cdot3^7\cdot1}\)

\(A=\dfrac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\)

\(=\dfrac{5.2^{30}.3^{18}-2^{29}.3^{20}}{5.2^{28}.3^{19}-7.2^{29}.3^{18}}\)

\(=\dfrac{2^2.3^{18}\left(5.2-3^2\right)}{2^{18}.3^{18}\left(5.2-3^2\right)}\)

\(=2\)

\(\dfrac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\)  (sửa \(-9^9\rightarrow.9^9\))

\(=\dfrac{5.2^{30}.3^{18}-2^2.3^{20}.2^{27}}{5.2^9.2^{19}.3^{19}-7.2^{29}.3^{18}}\)

\(=\dfrac{5.2^{30}.3^{18}-2^{29}.3^{20}}{5.2^{28}.3^{19}-7.2^{29}.3^{18}}\)

\(=\dfrac{2^{29}.3^{18}\left(15-9\right)}{2^{28}.3^{18}\left(15-14\right)}\)

\(=2.6=12\)