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, bạn coi đề coi có đúng ko

b,VT= 45¹⁰.5³⁰

=3¹⁰.3¹⁰.5¹⁰.5³⁰

=3²⁰.5⁴⁰

=3²⁰.5²⁰.5²⁰

=15²⁰.5²⁰

=75²⁰=>VP

cám ơn bạn

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

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)

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

=>12⁸.9¹²=18¹⁶

a) ...

b) 75^20 = 3^20 . 25^20 = 5^40 . 9^10 = 5^30.45^10