a)
100^{\frac{1}{2}}=\sqrt{100}=10
1000^{\frac{2}{3}}=((10)^3)^{\frac{2}{3}}=10^{3*\frac{2}{3}}=10^2
16^{0,75}=((2)^4)^{\frac{3}{4}}=2^3=8
{\frac{1}{27}}^{\frac{2}{3}}=(\frac{1}{3})^{3*\frac{2}{3}}=(\frac{1}{3})^2=\frac{1}{9}
(\frac{1}{32})^{0,4}=((\frac{1}{2})^5)^{\frac{2}{5}}=(\frac{1}{2})^2=\frac{1}{4}