Question

chứng tỏ rằng

75²⁰ = 45¹⁰.5³⁰

Answer 1

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

Answer 2

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

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

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