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 \(12^8.9^{12}=18^{16}\)

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

b)

Ta có:

\(75^{20}=45^{10}.5^{30}\\ hay\left(5^2.3\right)^{20}=\left(5.3^2\right)^{10}.5^{30}\\ 5^{40}.3^{20}=5^{10}.3^{20}.5^{30}\\ 5^{40}.3^{20}=5^{40}.3^{20}\)

Vậy \(75^{20}=45^{10}.5^{30}\left(ĐPCM\right)\)

Câu a hình như sai đề, không làm được

a)

a) 12⁸. 9¹² = 18¹⁶

biến đổi vế trái ta được :

12⁸ . 9¹² = (2² . 3)⁸ . (3²)¹²

= 2¹⁶ . 3⁸ . 3²⁴

= 2¹⁶ . 3³²

= 2¹⁶ . ( 3²)¹⁶

=[ 2 . ( 3²)]¹⁶

= (2 . 9)¹⁶

=18¹⁶

vế trái = vế phải

Vậy : 12⁸ . 9¹² = 18¹⁶