[latex]a)\ \frac{2^{-2}}{3^{-3}}*(frac{4}{9})^{2}=frac{2^{-2}}{3^{-3}}*frac{4^{2}}{9^{2}}=frac{2^{-2}*(2^{2})^2}{3^{-3}*(3^2)^2}=frac{2^{-2}*2^{4}}{3^{-3}*3^{4}}=frac{2^{-2+4}}{3^{-3+4}}=frac{2^{2}}{3^{1}}=frac{4}{3}= 1frac{1}{3}[/latex] [latex]b)\ \left ((frac{2}{3})^{-2} ight )^{-2}=left ( frac{2}{3} ight )^{(-2)*(-2)}=left ( frac{2}{3} ight )^{4}=frac{16}{81}[/latex] [latex]c)\ \frac{6^{0}+0^{6}}{6^{-1}}+(4^6-14^3)=frac{1+0}{6^{-1}}+(4^6-(4^2)^3)=\ \=1:(6^{-1})+(4^6-4^6)=1:frac{1}{6}+0=1*6=6[/latex] [latex]d)\ \left ( (frac{1}{3})^4*(frac{2}{3})^{-5} ight ):6^{-2}= frac{1}{81}*frac{243}{32} :frac{1}{6^{2}}=\ \=frac{3}{32} ight ):frac{1}{36}=frac{27}{32}*36=frac{27}{8}=3frac{3}{8}[/latex] [latex]e)\ \(0,5*8^6-2*16^4):7^3 =(frac{1}{2}*(2^3)^6)-2*(2^4)^4):7^{3}=\ \(2^{-1}*2^{18}-2*2^{16}):7^3=(2^{-1+18}-2^{1+16}):7^3=\ \=(2^{17}-2^{17}):7^3=0:7^3=0[/latex] [latex]f)\ \left ( (frac{5}{2})^3:(frac{2}{5})^2 ight )*(frac{5}{2})^{-4}=(frac{5}{2})^3*(frac{5}{2})^2 *(frac{5}{2})^{-4}=\ \=(frac{5}{2})^{3+2-4} =frac{5}{2}=2,5[/latex]
