d) [latex](32^{-frac12}:64^{frac34})^{frac12}*sqrt{128} = ((2^5)^{-frac12}:(2^6)^{frac34})^{frac12}*sqrt{2^7} =\\ (2^{-frac52}:2^{6*frac34})^{frac12}*(2^7)^{frac12} = (2^{-frac52*frac12}:2^{frac92*frac12})*2^{frac72} = \\(2^{-frac54}:2^{frac94})*2^{frac72} = 2^{-frac54-frac94+frac72} =2^{-frac{14}4+frac{14}4} = 2^0 [/latex] e) [latex]frac{3^{1frac12}*(frac13)^{1frac12}}{2^{2frac23}*(frac12)^{2frac23}}} = frac{(3*frac13)^{1frac12}}{(2*frac12)^{2frac23}} = frac{1^{1frac12}}{1^{2frac23}} = frac11 = 1= 2^0[/latex] f) [latex]frac{(frac12)^3*2^{-2}*sqrt[4]4}{64^{-frac34}*0,25} = frac{2^{-3}*2^{-2}*4^{frac14}}{(2^6)^{-frac34}*frac14} = frac{2^{-3-2}*(2^2)^{frac14}}{2^{-frac92}*4^{-1}} = \\frac{2^{-5}*2^{2*frac14}}{2^{-frac92}*(2^2)^{-1}} = frac{2^{-5}*2^{frac12}}{2^{-frac92}*2^{-2}} = 2^{-5+frac12-(-frac92)-(-2)} = 2^{-3+frac12+frac92} = 2^{-3+5} = 2^2[/latex]
