=\(\frac{5.2^{30}.3^{18}-2^2.3^{20}.2^{27}}{5.2^9.2^{19}.3^{19}-7.2^{29}.3^{18}}=\frac{5.2^{30}.3^{18}-2^{29}.3^{20}}{5.2^{28}.3^{19}-7.2^{29}.3^{18}}=\frac{2^{29}.3^{18}.\left(5.2-3^2\right)}{2^{28}.3^{18}\left(5.3-7.2\right)}=2\)

\(\frac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}=\frac{5.2^{30}.3^{18}-2^2.3^{20}.2^{27}}{5.2^9.3^{19}.2^{19}-7.2^{29}.3^{18}}\)

\(\frac{5.2^{30}.3^{18}-2^{29}.3^{20}}{5.2^{28}.3^{19}-7.2^{29}.3^{18}}=\frac{2^{29}.3^{18}.\left(2-9\right)}{7.2^{28}.3^{18}\left(3-2\right)}\)

\(\frac{-7.2^{29}.3^{18}}{7.2^{28}.3^{18}}=-1.2=-2\)

\(\frac{5.4^{15}.\left(-9\right)^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}=\frac{5.\left(2^2\right)^{15}.\left(-3^2\right)^9-2^2.3^{20}.\left(2^3\right)^9}{5.2^9.\left(2.3\right)^{19}-7.2^{29}.\left(3^3\right)^6}=\frac{-5.2^{30}.3^{18}-2^2.3^{20}.2^{27}}{5.2^9.2^{19}.3^{19}-7.2^{29}.3^{18}}=\frac{-5.2^{30}.3^{18}-2^{29}.3^{20}}{5.2^{28}.3^{19}-7.2^{29}.3^{18}}\)\(=\frac{-5.2^{30}.3^{18}-2^{29}.3^{20}}{5.2^{28}.3^{19}-7.2^{29}.3^{18}}=\frac{-2^{29}.3^{18}.\left(5.2+3^2\right)}{2^{28}.3^{18}.\left(5.3-7.2\right)}=\frac{-2^{29}.3^{18}.19}{2^{28}.3^{18}.1}=-2.19=-38\)

\(\frac{5.\left(2^2\right)^{15}.\left(-3^2\right)^9-2^2.3^{20}.\left(2^3\right)^9}{5.2^9.2^{19}.3^{19}-7.2^{29}.\left(3^3\right)^6}=\frac{5.2^{30}.-3^{18}-2^2.3^{20}.2^{27}}{5.2^{28}.3^{19}-7.2^{29}.3^{18}}=\frac{-5.2^{30}.3^{18}-2^{29}.3^{20}}{5.2^{28}.3^{19}-7.2^{29}.3^{18}}=\frac{-2^{29}.3^{18}.\left(5.2+3^2\right)}{2^{28}.3^{18}.\left(5.3-7.2\right)}=\frac{-2.29}{1}=-58\)

Đề như thế này chắc đúng hơn nhỉ?

\(\frac{5.14^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\)

Đặt   \(A=5.14^{15}.9^9-4.3^{20}.8^9\)  và  \(B=5.2^9.6^{19}-7.2^{29}.27^6\), ta được:

\(\text{+)}\)  \(A=5.14^{15}.9^9-4.3^{20}.8^9=5.\left(2^2\right)^{15}.\left(3^2\right)^9-2^2.3^{20}.\left(2^3\right)^9=5.2^{30}.3^{18}-2^2.3^{20}.2^{27}\)

         \(A=5.2^{30}.3^{18}-2^{29}.3^{20}=2^{29}.3^{18}\left(5.2-3^2\right)=2^{29}.3^{18}\)

\(\text{+)}\)  \(B=5.2^9.6^{19}-7.2^{29}.27^6=5.2^9.\left(2.3\right)^{19}-7.2^{29}.\left(3^3\right)^6=5.2^9.2^{19}.3^{19}-7.2^{29}.3^{18}\)

         \(B=5.2^{28}.3^{19}-7.2^{29}.3^{18}=2^{28}.3^{18}\left(5.3-7.2\right)=2^{28}.3^{18}\)

Do đó,  \(\frac{A}{B}=\frac{2^{29}.3^{18}}{2^{28}.3^{18}}=2\)

bai toán này ?

\(\frac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\)\(=\frac{5.2^{30}.3^{18}-2^2.3^{20}.2^{27}}{5.2^9.2^{19}.3^{19}-7.2^{29}.3^{18}}\)\(=\frac{5.2^{30}.3^{18}-2^{29}.3^{20}}{5.2^{28}.3^{19}-7.2^{29}.3^{18}}\)\(=\frac{2^{29}.3^{18}\left(5.2-3^2\right)}{2^{28}.3^{18}\left(5.3-7.2\right)}=\frac{2.1}{1}=2\)

học tốt ~~~

\(\frac{5\cdot4^{15}\cdot9^9-4\cdot3^{20}\cdot8^9}{5\cdot2^9\cdot6^{19}-7\cdot2^{29}\cdot27^6}\\ =2\)

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

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

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

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

\(=2.6=12\)

\(\frac{5\times4^{15}\times9^9-4\times3^{20}\times8^9}{5\times2^9\times6^{19}-7\times2^{29}\times27^6}\)

\(=\frac{5\times\left(2^2\right)^{15}\times\left(3^2\right)^9-2^2\times3^{20}\times\left(2^3\right)^9}{5\times2^9\times\left(2\times3\right)^{19}-7\times2^{29}\times\left(3^3\right)^6}\)

\(=\frac{5\times2^{30}\times3^{18}-2^2\times3^{20}\times3^{27}}{5\times2^9\times2^{19}\times3^{19}-7\times2^{29}\times3^{18}}\)

\(=\frac{2^{29}\times3^{18}\times\left(5\times2-3^2\right)}{2^{28}\times3^{18}\times\left(5\times3-7\times2\right)}\)

\(=2\)

Chúc bạn học tốt ^^

thanks

Ta có : \(\frac{5.4^{15}.9^9+4.3^{20}.\left(-8\right)^9}{5.2^9.6^{19}-7.2^{29}.27^6}=\frac{5.\left(2^2\right)^{15}.\left(3^2\right)^9-2^2.3^{20}.\left(2^3\right)^9}{5.2^9.\left(2.3\right)^{19}-7.2^{29}.\left(3^3\right)^6}=\frac{5.2^{30}.3^{18}-2^{29}.3^{20}}{5.2^{28}.3^{19}-7.2^{29}.3^{18}}\)

\(=\frac{2^{29}.3^{18}\left(5.2-3^2\right)}{2^{28}.3^{18}\left(5.3-7.2\right)}=\frac{2^{29}.3^{18}}{2^{28}.3^{18}}=2\)

Xét tử :

5.4¹⁵.9⁹ - 4.3²⁰.8⁹

= 5.2³⁰.3¹⁸ - 2² . 3²⁰ . 2²⁷

= 5 . 2³⁰ . 3¹⁸ - 2²⁹ . 3²⁰

= 3¹⁸ . 2²⁰ . ( 5 . 2¹⁰ - 2⁹ . 3² )

= 3¹⁸ . 2²⁰ . [ 2⁹ . ( 5 . 2 - 3² ) ]

= 3¹⁸ . 2²⁰ . 2⁹

= 3¹⁸ . 2²⁹

Xét mẫu :

5.2⁹.6¹⁹ - 7.2²⁹.27⁶

= 5 . 2⁹ . 2¹⁹ . 3¹⁹ - 7 . 2²⁹ . 3¹⁸

= 5 . 2²⁸ . 3¹⁹ - 7 . 2²⁹ . 3¹⁸

= 3¹⁸ . 2²⁸ . ( 5 . 3 - 7 . 2 )

= 3¹⁸ . 2²⁸

B = \(\frac{3^{18}.2^{29}}{3^{18}.2^{28}}=2\)