Question

hallar "n" $\sqrt[4]{\frac{\sqrt[3]{\frac{1}{x} } }{x} } = \sqrt{\sqrt[3]{\sqrt[4]{(\frac{1}{x})^{n} } } }$

Answer 1

n=8

Explicación paso a paso:

$\sqrt[4]{ \frac{ \sqrt[3]{ \frac{1}{x} } }{x} } = \sqrt{ \sqrt[3]{ \sqrt[4]{( \frac{1}{x} {)}^{n} } } }$

$\frac{ \sqrt[12]{ \frac{1}{x} } }{ \sqrt[4]{x} } = \sqrt[24]{( \frac{1}{x} {)}^{n} }$

$\frac{ \sqrt[12]{ {x}^{ - 1} } }{ \sqrt[4]{x} } = ( \frac{1}{x} {)}^{ \frac{n}{24} }$

$\sqrt[12]{ \frac{ {x}^{ - 1} }{ {x}^{3} } } = ( \frac{1}{x} {)}^{ \frac{n}{24} }$

$\sqrt[12]{ {x}^{ - 4} } = ( \frac{1}{x} {)}^{ \frac{n}{24} }$

${x}^{ - \frac{4}{12} } = ( \frac{1}{x} {)}^{ \frac{n}{24} }$

${x}^{ - \frac{1}{3} } = {x}^{ - \frac{n}{24} }$

$- \frac{1}{3} = - \frac{n}{24}$

$\frac{n}{24} = \frac{1}{3}$

$3n = 24$

$n = 8$

Mari espero me entiendas,no me salté ni un paso :)