a)
(3^{\frac{1}{2}} * 3^{-1,25}:3^{\frac{3}{4}})^{\frac{4}{3}}=(3^{0,5-1,25-0,75})^{\frac{4}{3}}=(3^{-1,5})^{\frac{4}{3}}=
(3^{-\frac{15}{10}})^{\frac{4}{3}}(3^{-\frac{3}{2}})^{\frac{4}{3}}=3^{-2}=(\frac{1}{3})^2=\frac{1}{9}
b)
(7^{-0,7}:7^{\frac{2}{5}}*7^{-0,9})^{\frac{1}{2}}=(7^{-0,7-0,4-0,9})^{\frac{1}{2}}=(7^{-2})^{\frac{1}{2}}=7^{-1}=\frac{1}{7}
d)
(0,5)^{-1}*4^{0,7}*(0,25)^{-0,3}=(\frac{1}{2})^{-1}*(2^2)^{0,7}*(\frac{1}{4})^{-0,3}=2^1*2^{1,4}*((\frac{1}{2})^2)^{-0,3}=
2^{2,4}*(2^{-2})^{-0,3}=2^{2,4}*2^{0,6}=2^3=8
e)
[4^{\frac{1}{3}}*(0,5)^{-\frac{1}{3}}]^{-2}=[4^{\frac{1}{3}}*(\frac{1}{2})^{-\frac{1}{3}}]^{-2}=[4^{\frac{1}{3}}*2^{\frac{1}{3}}]^{-2}=
(8^{\frac{1}{3}})^{-2}=[(2^3)^{\frac{1}{3}}]^{-2}=2^{-2}=(\frac{1}{2})^2=\frac{1}{4}