[tex]\displaystyle \bigg(4^{-1/4}+(\frac{1}{2^{-3/2}})^{-4/3}\bigg)*(4^{-0.25}-(2\sqrt{2})^{-4/3})=\\\\ \bigg(4^{-1/4}+(2^{3/2})^{-4/3}}\bigg)*(4^{-1/4}-(2^{3/2})^{-4/3})=\\\\=(4^{-1/4}+2^{-2})*(4^{-1/4}+2^{-2})=(4^{-1/4})^2-(2^{-2})^2=4^{-1/2}-2^{-4}=\\\\=\frac{1}{\sqrt{4}}-\frac{1}{2^4}=\frac{1}{2}-\frac{1}{16}=\frac{7}{16}[/tex]