a)
\frac{81^{\frac{1}{4}}+81^{\frac{3}{4}}}{81^{\frac{3}{4}}-81^{\frac{1}{4}}}=\frac{(3^4)^{\frac{1}{4}}+(3^4)^{\frac{3}{4}}}{(3^4)^{\frac{3}{4}}-(3^4)^{\frac{1}{4}}}=\frac{3+3^3}{3^3-3}=\frac{30}{24}=\frac{5}[4}=1\frac{1}{4}
b)
\frac{8^{\frac{2}{3}}+8^{\frac{1}{3}}}{8^{\frac{1}{3}}-8^{\frac{2}{3}}}=\frac{(2^3)^{\frac{2}{3}}+(2^3)^{\frac{1}{3}}}{(2^3)^{\frac{1}{3}}-(2^3)^{\frac{2}{3}}}=\frac{2^2+2}{2-2^2}=\frac{6}{-2}=-3
c)
\frac{4^{-\frac{1}{2}}+9^{-\frac{1}{2}}}{27^{-\frac{2}{3}}}=\frac{(2^2)^{-\frac{1}{2}}+(3^2)^{-\frac{1}{2}}}{(3^3)^{-\frac{2}{3}}}=\frac{2^{-1}+3^{-1}}{3^{-2}}=\frac{\frac{1}{2}+\frac{1}{3}}{(\frac{1}{3})^2}=\frac{\frac{3}{6}+\frac{2}{6}}{\frac{1}{9}}=
\frac{\frac{5}{6}}{\frac{1}{9}}=\frac{5}{6}*\frac{9}{1}=\frac{45}{6}=\frac{15}{2}=7,5