a) \(75^{20}=45^{10}.5^{30}\)

<=> \(5^{40}.3^{20}=5^{10}.3^{20}.5^{30}\)

<=> \(5^{40}.3^{20}=5^{10+30}.3^{20}\)

=> \(5^{40}.3^{20}=5^{40}.3^{20}\)

=> \(75^{20}=45^{10}.5^{30}\)

Hơi tóm tắt nên cậu suy tư tí nhé

45¹⁰.5³⁰

=(3².5)¹⁰.5³⁰

=(3²)¹⁰.5¹⁰.5³⁰

=3²⁰.5⁴⁰

=3²⁰.(5²)²⁰

=3²⁰.25²⁰

=(3.5)²⁰

=75²⁰

45¹⁰.5³⁰

=(3².5)¹⁰.5³⁰

=(3²)¹⁰.5¹⁰.5³⁰

=3²⁰.5⁴⁰

=3²⁰.(5²)²⁰

=3²⁰.25²⁰

=(3.5)²⁰

=75²⁰

\(12^8.9^{12}=\left(2^2.3\right)^8.\left(3^2\right)^{12}=2^{16}.3^8.3^{24}=2^{16}.\left(3^2\right)^{16}=2^{16}.9^{16}\left(2.9\right)^{16}=18^{16}\)

a, 12⁸.9¹²

=(2².3)⁸.(3²)¹²

=2¹⁶.3⁸.3²⁴

=2¹⁶.3⁸.3¹⁶.3⁸

=(2.3)¹⁶.(3²)⁸

=6¹⁶.3¹⁶

=(6.3)¹⁶

=18¹⁶

75²⁰

=(5².3)²⁰

=5⁴⁰.3²⁰

=5³⁰.5¹⁰.(3²)¹⁰

=5³⁰.5¹⁰.9¹⁰

=5³⁰.(5.9)¹⁰

=5³⁰.45¹⁰

75²⁰ = 45¹⁰ . 5³⁰ (Vế phải)

Vế phải = 45¹⁰ . 5³⁰

= 5¹⁰ . 9¹⁰ 5³⁰

= 5⁴⁰ . 9¹⁰

= (5²)²⁰ . (3²)¹⁰

= 25²⁰ . 3²⁰

= 75²⁰

\(75^{20}=\left(3\cdot25\right)^{20}=3^{20}\cdot25^{20}=3^{20}\cdot5^{40}\)

\(45^{10}\cdot5^{30}=\left(9\cdot5\right)^{10}\cdot5^{30}=9^{10}\cdot5^{10}\cdot5^{30}=3^{20}\cdot5^{40}\)

=> đpcm 

@_@ học tốt ^^

Có : 45^10 x 5^30 = 5^10 x 9^10 x 5^30 = 5^40 x 9^10 = (5^2)^20 x (3^2)^20 = 25^20 x 3^20 = (25 x 3)^20 = 75^20

=> ĐPCM

k mk nha

Ta có: 75^20 = ( 75^2 )^10 = 5625^10

           5^30 = ( 5^3 )^10 = 125^10

=> 45^10 * 125^10 = ( 45 * 125 )^10 = 5625^10

=> 75^20 = 45^10 * 5^30

CaM mon bn nhiu nha

Mk k pk lm j cho bn ca mk ms vo thoi

25x4+75x+7x25/5-10+15-20+25-30+35-40+45=2720

Ta có :

\(75^{10}.75^{10}=\left(5^{10}.3^{10}.3^{10}\right).\left(5^{10}.5^{10}.5^{10}\right)\)

\(75^{10}.75^{10}=\left(5^{10}.5^{10}.3^{10}\right).\left(5^{10}.5^{10}.3^{10}\right)\)

\(75^{10}.75^{10}=75^{10}.75^{10}\)

Vì vậy : \(75^{20}=45^{10}.5^{30}\)

\(75^{20}=3^{20}.5^{40}\)

\(45^{10}.5^{30}=3^{20}.5^{40}\)

Do đó:\(75^{20}=45^{10}.5^{30}\)(đpcm)