\(\dfrac{27^{15}.5^3.8^4}{25^2.81^{11}.2^{11}}\)
= \(\dfrac{\left(3^3\right)^{15}.5^3.\left(2^3\right)^4}{\left(5^2\right)^2.\left(3^4\right)^{11}.2^{11}}\)
= \(\dfrac{3^{45}.5^3.2^{12}}{5^4.3^{44}.2^{11}}\)
= \(\dfrac{3.1.2}{5.1.1}\)
= \(\dfrac{6}{5}\)