Question

01) Simplifique a expressão abaixo:
$\mathtt{\huge\sf{\dfrac{\sqrt[5]{{x^2}\sqrt[3]{x^4\sqrt{x^7}}}}{\sqrt[{3}]{\dfrac{\sqrt[4]{\dfrac{\sqrt[5]{\dfrac{1}{{x^6}}}}{x}}}{x^2}}}}}$

Answer 1

Resposta:

$\sqrt[4]{x^{7}}$

Explicação passo a passo:

$Numerador:\\\\1)\sqrt{x^{7}}=x^{\frac{7}{2} }\\\\2)x^{4}*x^{\frac{7}{2} }=x^{\frac{15}{2} }\\\\3)\sqrt[3]{x^{\frac{15}{2} }}=x^{\frac{15}{6} }\\\\4) x^{2}*x^{\frac{15}{6} }=x^{\frac{27}{6} }\\\\5)\sqrt[5]{x^{\frac{27}{6} }}=x^{\frac{27}{30} }$

$Denominador:\\\\1)\sqrt[5]{\frac{1}{x^{6}} }=\frac{1}{\sqrt[5]{x^{6}} }=x^{-\frac{6}{5} }\\\\2) \sqrt[4]{\frac{x^{-\frac{6}{5} }}{x} }=\sqrt[4]{x^{-\frac{11}{5} }}=x^{-\frac{11}{20} }\\\\3)\sqrt[3]{\frac{x^{-\frac{11}{20} }}{x^{2}} }=\sqrt[3]{x^{-\frac{51}{20} }}=x^{-\frac{51}{60} }$

$Resultado:\\\\\frac{x^{27/30}}{x^{-51/60}}=x^{105/60}=x^{7/4}=\sqrt[4]{x^{7}}$