\(\dfrac{14^{1005}\cdot5^{1006}}{2^{1007}\cdot35^{1004}}=\dfrac{7^{1005}\cdot2^{1005}\cdot5^{1006}}{2^{1007}\cdot5^{1004}\cdot7^{1004}}\)
\(=\dfrac{7^{1005}}{7^{1004}}\cdot\dfrac{2^{1005}}{2^{1007}}\cdot\dfrac{5^{1006}}{5^{1004}}\)
\(=\dfrac{7}{2^2}\cdot5^2=7\cdot\dfrac{25}{4}=\dfrac{175}{4}\)
`(14^1005 . 5^1006)/(2^1007 . 35^1004) `
`= (2^1005 . 7^1005 . 5^1006)/(2^1007 . 5^1004 . 7^1004) `
`= (1 . 7 . 5^2)/(2^2 . 1 .1) `
`= (7 . 25)/4`
`= 175/4`
\(\dfrac{14^{1005}.5^{1006}}{2^{1007}.35^{1004}}=\dfrac{\left(7.2\right)^{1005}.5^{1006}}{2^{1007}.\left(7.5\right)^{1004}}=\dfrac{7^{1005}.2^{1005}.5^{1006}}{2^{1007}.7^{1004}.5^{1004}}=\dfrac{7.5^2}{2^2.5}=\dfrac{7.25}{4}=\dfrac{175}{4}\)
