[latex]frac{(8cdot3)^{10}}{27^{3}:32^{-6}} = frac{(2^{3})^{10}cdot3^{10}}{(3^{3})^{3}:(2^{5})^{-6}}=frac{2^{30}cdot3^{10}}{3^{9}cdot(2^{-30})^{-1}} = frac{2^{30}cdot3^{10}}{3^{9}cdot2^{30}} = 3^{10-9} = 3^{1} = 3[/latex]