Question

Chứng minh rằng:

75²⁰=45¹⁰.5³⁰

 

Answer 1

45¹⁰.5³⁰=3²⁰.5¹⁰.5³⁰=3²⁰.5⁴⁰=3²⁰.(5²)²⁰=75²⁰

->điều phải chứng minh.

Answer 2

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

Vậy \(75^{20}=45^{10}.5^{30}\left(=5^{40}.3^{20}\right)\)