Question

Chứng min đẳng thức sau đây 

75²⁰=45¹⁰.5³⁰

Answer 1

\(75^{20}=45^{10}\cdot5^{30}=45^{10}\cdot125^{10}=5625^{10}=75^{20}\)

Answer 2

\(75^{20}=\left(3.5^2\right)^{20}\)

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

\(=\left(3^2\right)^{10}.5^{10}.5^{10}.5^{20}\)

\(=\left(3^2.5\right)^{10}.5^{30}\)

\(=\left(5.9\right)^{10}.5^{30}\)

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

Vậy \(75^{20}=45^{10}.5^{30}\)