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1. [latex] \frac{0.1^{-1}-(0.4)^0}{2 \frac{2}{3} *( \frac{2}{3} )^{-3}+(- \frac{1}{3} )^{-1}} =(10-1):( \frac{8}{3}* \frac{27}{8} +(-3) )=9:(9-3 )=9:6=1.5[/latex] 2. [latex] \frac{1^{-1}+2^{-2}}{( \frac{2}{3} )^{-2}+(-4)^{-1}*5+0.5^{-2}} =(1+ \frac{1}{4} ):( \frac{9}{4} -\frac{1}{4}*5+4 )= \frac{5}{4} :( \frac{9}{4} - \frac{5}{4}+4 )= \\ =\frac{5}{4} :5= \frac{5*1}{4*5} = \frac{1}{4} =0.25[/latex] 3. [latex] \frac{9*3^{-2}+4*( \frac{2}{3})^{-2} }{(-3)^0+(-0.5)^0*( \frac{1}{81})^{- \frac{1}{2} } } =(1+4* \frac{9}{4} ):(1+1*9)=10:10=1[/latex] 4. [latex] \frac{( \frac{1}{9} )^{-3}*81^2*( \frac{1}{9} )^4+( \frac{1}{6} )^{-4}}{225^{ \frac{1}{2} }:(7.5)^0} =(9^3*9^4*( \frac{1}{9^4} )+6^4):(15)= \frac{9^3+6^4}{15} =135[/latex]