a)
2^{\frac{1}{2}}*32^{\frac{1}{2}}+72^{\frac{1}{3}}:9^{\frac{1}{3}}=(2*32)^{\frac{1}{2}}+(72:9)^{\frac{1}{3}}=64^{\frac{1}{2}}+8^{\frac{1}{3}}=\sqrt{64}+\sqrt[3]8=8+2=10
b)
48^{\frac{1}{2}}*3^{\frac{1}{2}}+25^{\frac{1}{3}}*5^{\frac{1}{3}}=(48*3)^{\frac{1}{2}}+(25*5)^{\frac{1}{3}}=144^{\frac{1}{2}}+125^{\frac{1}{3}}=\sqrt{144}+(5^3)^{\frac{1}{3}}=12+5=17
c)
108^{\frac{1}{2}}:3^{\frac{1}{2}}-3^{\frac{1}{4}}*27^{\frac{1}{4}}=(108:3)^{\frac{1}{2}}-(3*27)^{\frac{1}{4}}=36^{\frac{1}{2}}-81^{\frac{1}{4}}=\sqrt{36}-(3^4)^{\frac{1}{4}}=6-3=3
d)
2^{\frac{1}{2}}*50^{\frac{1}{2}}-2^{\frac{1}{5}}*16^{\frac{1}{5}}=(2*50)^{\frac{1}{2}}-(2*16)^{\frac{1}{5}}=100^{\frac{1}{2}}-32^{\frac{1}{5}}=\sqrt{100}-(2^5)^{\frac{1}{5}}=10-2=8
e)
(27^{\frac{1}{6}})^{-2}=27^{-\frac{1}{3}}=(3^3)^{-\frac{1}{3}}=3^{-1}=\frac{1}{3}
f)
(49^{\frac{1}{5}})^{-\frac{5}{2}}=49^{-\frac{1}{2}}=(7^2)^{-\frac{1}{2}}=7^{-1}=\frac{1}{7}