Resposta:
[tex]\sqrt[4]{x^{7}}[/tex]
Explicação passo a passo:
[tex]Numerador:\\\\1)\sqrt{x^{7}}=x^{\frac{7}{2} }\\\\2)x^{4}*x^{\frac{7}{2} }=x^{\frac{15}{2} }\\\\3)\sqrt[3]{x^{\frac{15}{2} }}=x^{\frac{15}{6} }\\\\4) x^{2}*x^{\frac{15}{6} }=x^{\frac{27}{6} }\\\\5)\sqrt[5]{x^{\frac{27}{6} }}=x^{\frac{27}{30} }[/tex]
[tex]Denominador:\\\\1)\sqrt[5]{\frac{1}{x^{6}} }=\frac{1}{\sqrt[5]{x^{6}} }=x^{-\frac{6}{5} }\\\\2) \sqrt[4]{\frac{x^{-\frac{6}{5} }}{x} }=\sqrt[4]{x^{-\frac{11}{5} }}=x^{-\frac{11}{20} }\\\\3)\sqrt[3]{\frac{x^{-\frac{11}{20} }}{x^{2}} }=\sqrt[3]{x^{-\frac{51}{20} }}=x^{-\frac{51}{60} }\\\\[/tex]
[tex]Resultado:\\\\\frac{x^{27/30}}{x^{-51/60}}=x^{105/60}=x^{7/4}=\sqrt[4]{x^{7}}[/tex]
