[tex]\dfrac{36^6}{27^5\cdot8^5}=\dfrac{4^6\cdot9^6}{(3^3)^5\cdot(2^3)^5}=\dfrac{(2^2)^6\cdot(3^2)^6}{2^{15}\cdot3^{15}}=\\\\\\=\dfrac{2^{12}\cdot3^{12}}{2^{15}\cdot3^{15}}=\dfrac{2^{12}}{2^{15}}\cdot\dfrac{3^{12}}{3^{15}}=2^{-3}\cdot3^{-3}=\\\\\\=(2\cdot3)^{-3}=6^{-3}=(\dfrac{1}{6})^3}=\dfrac{1}{216}[/tex]
