[latex] \sqrt[4]{x \sqrt{x \sqrt[3]{x} } } [/latex] При х= [latex] \sqrt[5]{ 8^{4} } [/latex]

[latex]\sqrt[4]{x\sqrt{x\sqrt[3]{x}}}=\sqrt[4]{\sqrt{x^2\cdot x\sqrt[3]{x}}}=\sqrt[4\cdot 2]{x^3\sqrt[3]x}=\sqrt[8]{\sqrt[3]{x^{3\cdot3}\cdot x}}=\\\\=\sqrt[8\cdot3]{x^9\cdot x}=\sqrt[24]{x^{10}}=x^{\frac{10}{24}}=x^{\frac{5}{12}}=\sqrt[12]{x^5};\\\\\\x=\sqrt[5]{8^4},\\\\\sqrt[12]{x^5}=\sqrt[12]{\left(\sqrt[5]{8^4}\right)^5}=\sqrt[12]{8^4}=8^{\frac{4}{12}}=8^{\frac{1}{3}}=\sqrt[3]8=\sqrt[3]{2^3}=2.\\\\OTBET:\ 2.[/latex]