\(=\dfrac{5\cdot2^{30}\cdot3^{18}-2^{29}\cdot3^{20}}{5\cdot2^{29}\cdot3^{19}-7\cdot2^{29}\cdot3^{18}}=\dfrac{2^{29}\cdot3^{18}\left(5\cdot2-3^2\right)}{2^{29}\cdot3^{18}\left(5\cdot3-7\right)}=\dfrac{10-9}{15-7}=\dfrac{1}{8}\)

Đề bài sai chỗ ... - 9⁹ nhé, nếu là .9⁹ sẽ hợp lí hơn =))

\(A=\frac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^{10}.6^{19}-7.2^{29}.27^6}=\frac{5.\left(2^2\right)^{15}\left(3^2\right)^9-2^2.3^{20}.\left(2^3\right)^9}{5.2^{10}.\left(2.3\right)^{19}-7.2^2.\left(3^2\right)^6}\)

\(A=\frac{5.2^{30}.3^{18}-2^2.3^{20}.2^{27}}{5.2^{10}.2^{19}.3^{19}-7.2^{29}.3^{18}}\)

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

\(A=\frac{2^{29}.3^{18}.\left(5.2-3^2\right)}{2^{29}.3^{18}.\left(5.3-7\right)}\)

\(A=\frac{10-9}{15-7}=\frac{1}{8}\)

\(\frac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^{10}.6^{19}-7.2^{29}.27^6}=\frac{5.2^{30}.3^{18}-3^{20}.2^{29}}{5.2^{29}.3^{19}-7.2^{29}.3^{18}}\)

\(=\frac{2^{29}.3^{18}.\left(5.2-9\right)}{2^{29}.3^{18}.\left(5.3-7\right)}=1\)

5.4¹⁵.9⁹-4.3²⁰.8⁹                             5.2³⁰.3¹⁸-2².3²⁰.2²⁷                            5.2³⁰.3¹⁸-2².3²⁰.2²⁷                5.2³⁰.3¹⁸-2².2²⁷.3²⁰  

^{------------------------}                  = --------------------------------------   =        --------------------------------------  =--------------------------------------

5.2¹⁰.6¹⁹-7.2²⁹.27⁶                    5.2¹⁰.(2.3)¹⁹-7.2²⁹.3¹⁸                          5.2¹⁰.2¹⁹.3¹⁹-7.2²⁹.3¹⁸         5.2²⁹.3¹⁹-7.2²⁹.3¹⁸

                                                                                                                                  =       5.2³⁰.3¹⁸-2²⁹.3²⁰    

                                                                                                                                      --------------------------------------

                                                                                                                                            5.2²⁹.3¹⁹-7.2²⁹.3¹⁸

                                                                             làm nốt nha!!

\(\frac{5.4^{15}.9^9-4.3^{20}.8^9}{5\cdot2^{10}\cdot6^{19}-7.2^{29}.27^6}\) 

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

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

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

\(=\frac{2.\left(10-9\right)}{15-14}\) 

\(=2\) 

Vậy BT trên có giá trị là: 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 = \(\frac{3^{18}.2^{29}}{3^{18}.2^{28}}=2\)

\(\dfrac{5.4^{15}.9^9+4.3^{20}.8^9}{5.2^{10}.6^{19}-7.2^{29}.27^6}=\dfrac{5.2^{30}.3^{18}+2^2.3^{20}.2^{27}}{5.2^{10}.2^{19}.3^{19}-7.2^{29}.3^{18}}\)

=\(\dfrac{5.2^{30}.3^{18}+2^{29}.3^{20}}{5.2^{29}.3^{19}-7.2^{29}.3^{18}}=\dfrac{2^{29}.3^{18}\left(5.2+3^2\right)}{2^{29}.3^{18}\left(5.3-7\right)}\)

=\(\dfrac{10+9}{15-7}=\dfrac{19}{8}\)

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

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

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

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

\(=2.6=12\)