\(\dfrac{2018^{2019}.4^{2018}}{1009^{2019}.8^{2019}}\)
=\(\dfrac{2018^{2019}.4^{2018}}{1009^{2019}.\left(2.4\right)^{2019}}\)
=\(\dfrac{2018^{2019}.4^{2018}}{1009^{2019}.2^{2019}.4^{2019}}\)
=\(\dfrac{2018^{2019}.4^{2018}}{\left(1009.2\right)^{2019}.4^{2019}}\)
=\(\dfrac{2018^{2019}.4^{2018}}{2018^{2019}.4^{2019}}\)
=\(\dfrac{1}{4}\)