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[latex]dfrac{log_327-log_31}{3^{-2}*3^8}=dfrac{log_3(27:1)}{3^{-2+8}}=dfrac{log_327}{3^{6}}=dfrac{log_33^3}{3^{6}}=\ \ =dfrac{3}{3^6}=3^{1-6}=3^{-5}=oxed{dfrac{1}{243}}[/latex]

[latex]frac{log_{3}27-log_{3}1}{3^{-2}cdot3^{8}} = frac{log_{3}frac{27}{1}}{3^{-2+8}}=frac{log_{3}3^{3}}{3^{6}} = frac{3}{3^{6}} =3^{1-6} = 3^{-5} = (frac{1}{3})^{5} = frac{1}{243}[/latex]