Question

35. Escreva em forma de potência
$\sqrt{ \frac{x}{ \sqrt[5]{ {x}^{4} } } }$


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Answer 1

Propriedades usadas

$\sqrt[b]{a^c}=a^{\frac{c}{b}}$

$\dfrac{a^c}{a^b}=a^{c-b}$

Solução:

$\sqrt{\dfrac{x}{\sqrt[5]{x^4}}}\\\\\sqrt{\dfrac{x^1}{x^{\frac{4}{5}}}}\\\\\sqrt{x^{1-\frac{4}{5}}}\\\\\sqrt{x^{\frac{5-4}{5}}}\\\\\sqrt[2]{x^{\frac{1}{5}}}\\\\x^{\frac{1}{5}\cdot\frac{1}{2}}\\\\\boxed{x^{\frac{1}{10}}}$