a)
49^{\frac{1}{2}}+16^{\frac{3}{4}}=(7^2)^{\frac{1}{2}}+(2^4)^{\frac{3}{4}}=7+2^3=7+8=15
27^{\frac{2}{3}}-81^{\frac{1}{4}}=(3^3)^{\frac{2}{3}}-(3^4)^{\frac{1}{4}}=3^2-3=6
32^{-\frac{3}{5}}-32^{\frac{3}{5}}=(2^5)^{-\frac{3}{5}}-(2^5)^{\frac{3}{5}}=2^{-3}-2^3=\frac{1}{2^3}-8=\frac{1}{8}-8=-7\frac{7}{8}
b)
81^{\frac{1}{2}}+\sqrt[3]{8}-32^{\frac{3}{5}}+32^{-\frac{1}{5}}=(3^4)^{\frac{1}{2}}+\sqrt[3]{2^3}-(2^5)^{\frac{3}{5}}+(2^5)^{-\frac{1}{5}}=
3^2+2-2^3+2^{-1}=3+\frac{1}{2}=3\frac{1}{2}
16^{\frac{3}{4}}+16^{\frac{1}{4}}-81^{-\frac{3}{4}}=(2^4)^{\frac{3}{4}}+(2^4)^{\frac{1}{4}}-(3^4)^{-\frac{3}{4}}=2^3+2-3^{-3}=10-\frac{1}{3^3}=10-\frac{1}{27}=9\frac{26}{27}
c)
9^{\frac{1}{2}}-\sqrt[4]{16}+81^{\frac{1}{4}}-3^{-2}=(3^2)^{\frac{1}{2}}-\sqrt[4]{2^4}+(3^4)^{\frac{1}{4}}-(\frac{1}{3})^2=3-2+3-\frac{1}{9}=3\frac{8}{9}
(\frac{36}{49})^{-\frac{1}{2}}-8^{\frac{2}{3}}+(\sqrt{16})^{-1}-(27^{\frac{1}{2}})^0=\sqrt{\frac{49}{36}}-(2^3)^{\frac{2}{3}}+4^{-1}-1=\frac{7}{6}-2^2+\frac{1}{4}-1=
2\frac{5}{6}+\frac{1}{4}-1=-2\frac{10}{12}+\frac{3}{12}-1=-2\frac{7}{12}-1=-3\frac{7}{12}