Ta có : \(5^7.25^7=5^7.\left(5^2\right)^7=5^7.5^{14}=5^{21}\)
\(625^6=\left(5^4\right)^6=5^{24}\)
mà 21 < 24
\(\Rightarrow5^{21}< 5^{24}\)
\(\Rightarrow5^7.25^7< 625^6\)
57. 257 và 6256
57. 257 = ( 5 . 25 )7= 1257= 1256.125
6256 = (125.5)6 = 1256 . 5 6= 1256. 15625
vì 125 < 15625 => 57. 257 < 6256
\(5^7\cdot25^7=\left(5+25\right)^7=25^3\cdot25^7\cdot5=25^{10}\cdot5=5^{21}\)
\(625^6=\left(25\cdot25\right)^6=\left(5^2\cdot5^2\right)^6=25^{24}=5^{48}\)
\(5^7\cdot25^7< 625^6\)
