Ta có: \(30\cdot10^8\cdot5^4-25^6\cdot16^2\cdot3\)
\(=2\cdot3\cdot5\cdot2^8\cdot5^8\cdot5^4-5^{12}\cdot2^8\cdot3\)
\(=2^9\cdot3\cdot5^{13}-2^8\cdot3\cdot5^{12}=2^8\cdot3\cdot5^{12}\left(2\cdot5-1\right)=2^8\cdot3^3\cdot5^{12}\)
\(75^3\cdot20^4+3^3\cdot5^{10}\cdot32^2\)
\(=\left(5^2\cdot3\right)^3\cdot\left(2^2\cdot5\right)^4+3^3\cdot5^{10}\cdot2^{10}\)
\(=5^6\cdot3^3\cdot2^8\cdot5^4+3^3\cdot5^{10}\cdot2^{10}=3^3\cdot2^8\cdot5^{10}\left(1+5^2\right)=3^3\cdot2^9\cdot5^{10}\cdot13\)
Ta có: \(\frac{30\cdot10^8\cdot5^4-25^6\cdot16^2\cdot3}{75^3\cdot20^4+3^3\cdot5^{10}\cdot32^2}\)
\(=\frac{2^8\cdot3^3\cdot5^{12}}{3^3\cdot2^9\cdot5^{10}\cdot13}=\frac12\cdot\frac{5^2}{13}=\frac12\cdot\frac{25}{13}=\frac{25}{26}\)
