Question

$(sqrt[3]{49}- 7^{-1/2})/ (( sqrt[6]{49}) ^{2} * sqrt{7} *x)= frac{1}{7} ^{2} * ( frac{1}{ sqrt[4]{49} } ) ^{2}$

Answer 1

$sqrt[3]{49}*7^{-1/2} = 7^{2/3-1/2} =7^{4/6-3/6} =7^{1/6}$
$sqrt[6]{49^2} * sqrt{7} = sqrt[3]{49} * sqrt{7} =7^{2/3+1/2}=7^{4/6+3/6}=7^{7/6}$
$(1/7)^2* (frac{1}{ sqrt[4]{49} } )^2=1/49*(1/ sqrt{49} )=1/7^2*1/7=1/7^3=7^{-3}$
Подставляем все это в уравнение
$frac{7^{1/6}}{7^{7/6}*x} =7^{-3}$
$1/(7x)=1/7^3$
$x=7^2=49$