\(\dfrac{14^{1005}}{2^{1007}}\cdot\dfrac{5^{1006}}{25^{1004}}\)
\(=\dfrac{2^{1005}\cdot7^{1005}\cdot5^{1006}}{2^{1007}\cdot5^{2008}}\)
\(=\dfrac{7^{1005}}{2^2\cdot5^{1002}}\)
\(\dfrac{14^{1005}}{2^{1007}}.\dfrac{5^{1006}}{35^{1004}}=\dfrac{2^{1005}.7^{1005}.5^{1006}}{2^{1007}.7^{1004}.5^{1004}}=\dfrac{7.5^2}{2^2}=\dfrac{175}{4}\)
\(\dfrac{14^{1005}}{2^{1007}}.\dfrac{5^{1006}}{35^{1004}}\)
\(=\dfrac{\left(2.7\right)^{1005}.5^{1006}}{2^{1007}.\left(5.7\right)^{1004}}\)
\(=\dfrac{2^{1005}.7^{1005}.5^{1006}}{2^{1007}.5^{1004}.7^{1004}}\)
\(=\dfrac{7.5^2}{2^2}=\dfrac{175}{4}\)
