\(75^{20}=45^{10}.5^{30}\)
\(45^{10}.5^{30}\)
=\(\left(3^2.5\right)^{10}.5^{10+20}\)
= \(\left(3^2\right)^{10}.5^{10}.5^{30}\)
= \(3^{20}.5^{40}\)
= \(3^{20}.\left(5^2\right)^{20}\)
= \(3^{20}.25^{20}\)
= \(75^{20}\)
\(45^{10}\times5^{30}\)
\(=\left(3^2\times5\right)^{10}\times5^{30}\)
\(=\left(3^2\right)^{10}\times5^{10+30}\)
\(=3^{20}\times25^{20}\)
\(=75^{20}\)ĐPCM
Ta có: 7520 = 752.10 = (752) 10 = 562510
530 = 53.10 = (53) 10 = 125 10
Vậy 4510 x 12510 = ( 45x125)10 = 562510
=> 7520 = 4510 x 530
\(45^{10}\cdot5^{30}=\left(9.5\right)^{10}\cdot5^{30}=9^{10}\cdot5^{10}\cdot5^{30}=9^{10}\cdot5^{40}=9^{10}\cdot5^{4\cdot10}=9^{10}\cdot625^{10}=\left(9.625\right)^{10}5625^{10}\)\(=\left(75^2\right)^{10}=75^{20}\)
