\(12^8.9^{12}=4^8.3^8.9^{12}=2^{16}.9^4.9^{12}=2^{16}.9^{16}=\left(2.9\right)^{16}=18^{16}\left(đpcm\right)\)

\(12^8.9^{12}=(3.2^2)^8.(3^2)^{12}\)

\(=3^8.2^{16}.3^{24}=2^{16}.3^{8+24}=2^{16}.3^{32}\)

\(=2^{16}.9^{16}=(2.9)^{16}=18^{16}\)

Chứng minh : 

12^8 . 9^12 = 18^16 

Biến đổi VT ( vế trái ) : 12^8 . 9^12 = ( 2^2 . 3 )^8 . ( 3^2 )^12

                                                             = 2^16 .3^8 . 3^24 = 2^16 . 3^32 

Biến đổi VP ( vế phải )  : 18^16 = ( 2 . 3^2 )^16 = 2^16 . 3^32 

Vậy VT = VP   

12⁸.9¹²=(2².3)⁸.(3²)¹²=2¹⁶.3⁸.3²⁴=2¹⁶.3³²=2¹⁶.(3²)¹⁶=2¹⁶.9¹⁶=(2.9)¹⁶=18¹⁶

=>12⁸.9¹²=18¹⁶

\(12^8.9^{12}=\left(2^2.3\right)^8.\left(3^2\right)^{12}=2^{16}.3^8.3^{24}=2^{16}.3^{32}=2^{16}.\left(3^2\right)^{16}=2^{16}.9^{16}=18^{16}\)

a) Ta có : \(45^{10}=5^{10}.3^{20}\)

\(\Rightarrow45^{10}.5^{30}=3^{20}.5^{10}.5^{30}=3^{20}.5^{40}=3^{20}.\left(5^2\right)^{20}=3^{20}.25^{20}=\left(3.25\right)^{20}=75^{20}\)

Vậy \(45^{10}.5^{30}=75^{20}\)

b) Ta có : \(12^8=3^8.2^{16}\)và  \(9^{12}=3^{24}\)

\(\Rightarrow12^8.9^{12}=3^8.2^{16}.3^{24}=2^{16}.\left(3^2\right)^{16}=2^{16}.9^{16}=\left(2.9\right)^{16}=18^{16}\)

Vậy \(12^8.9^{12}=18^{16}\)

Ta có:+, 12^8. 9^12 = (12^2)^4. (3^3)^4

                             =144^4. 27^4       

                             = 3888^4

           +, 18^16 = (18^4)^4

                         = 104976^4

           Vì 3888^4 < 104976^4 nên 12^8. 9^12< 18^16

                                Vậy 12^8 . 9^12 < 18^16

a) \(12^8.9^{12}=18^{16}\)

ta cóvế trái : \(12^8.9^{12}=\left(2^2.3\right)^8.\left(3^2\right)^{12}=2^{16}.3^8.3^{24}=2^{16}.3^{32}\)

vế phải :\(18^{16}=\left(2.3^2\right)^{16}=2^{16}.3^{32}\)

=> VT =VP

b) \(75^{20}=45^{10}.5^{30}\)

VT=\(75^{20}=\left(3.5^2\right)^{20}=3^{20}.5^{40}\)

VP = \(45^{10}.5^{30}=\left(2^2.5\right)^{10}.5^{30}=2^{20}.5^{30}\)

ta tháy VT=VP

=> ĐPCM

\(12^8.9^{12}=3^8.\left(2^2\right)^8.9^{12}=9^4.2^{16}.9^{12}=2^{16}.9^{16}=\left(2.9\right)^{16}=18^{16}\)

nên bạn ghi thiếu đề nha, 18¹⁶ mới đúng