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

[latex]7 ^{2/3}*7 ^{-1/2}/7 ^{2/3} *7 ^{1/2}=7 ^{-2}*7 ^{-1} [/latex] [latex]1/7x=1/7^3[/latex] 7x=7³ x=7² x=49

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