Question

 найдите значения выражения

$(4^{-frac{1}{4} }+(frac{1}{2^-frac{3}{2} } )^{-frac{4}{3} })*(4^{-0.25}-(2sqrt{2})^{(-frac{4}{3}) } )$

Answer 1

$(4^{-frac{1}{4}}+(frac{1}{2^{-frac{3}{2}}})^{-frac{4}{3}})*(4^{-0.25}-(2sqrt{2})^{(-frac{4}{3})})=$

 

$=(4^{-frac{1}{4}}+(2^{frac{3}{2}})^{-frac{4}{3}})*((4^{-frac{1}{4}}-(2^{frac{3}{2}})^{-frac{4}{3}})=$ 

 

$=(4^{-frac{1}{4}}+(2^{-2})*(4^{-frac{1}{4}}-(2^{-2})=(4^{-frac{1}{4}})^{2}-(2^{-2})^{2}=$

 

$=4^{-frac{1}{2}}-2^{-4}=frac{1}{2}-frac{1}{16}=frac{7}{16}$ 

Answer 2

$(4^{-frac{1}{4}}+(frac{1}{2^{-frac{3}{2}}})^{-frac{4}{3}}) (4^{-0.25}-(2sqrt{2})^{-frac{4}{3}})=\ =(2^{-frac{1}{2}}+(2^{frac{3}{2}}})^{-frac{4}{3}}) (2^{-0.5}-(2^1*2^{frac{1}{2}})^{-frac{4}{3}})=\ =(2^{-frac{1}{2}}+2^{frac{3}{2}*(-frac{4}{3})}) (2^{-frac{1}{2}}-2^{frac{3}{2}*(-frac{4}{3})})=\ =(2^{-frac{1}{2}*2}-2^{-2*2})=2^{-1}-2^{-4}=\ =frac{1}{2}-frac{1}{16} = frac{8-1}{16} = frac{7}{16}$