(\sqrt{5^{-1}}*8^{\frac{1}{6}}*0,09^{\frac{1}{4}})^2=((\frac{1}{5})^{\frac{1}{2}}*(2^3)^{\frac{1}{6}}*(0,3^2)^{\frac{1}{4}})^2=((\frac{1}{5})^{\frac{1}{2}}*2^{\frac{1}{2}}*(\frac{3}{10})^{\frac{1}{2}})^2=
((\frac{1}{5}*2*\frac{3}{10})^{\frac{1}{2}})^2=((\frac{1}{5}*\frac{3}{5})^{\frac{1}{2}})^2=(\frac{3}{5^2})^1=\frac{3}{25}