Question

$\sqrt[4]{ \frac{1}{256} ?}$
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Answer 1

Resposta:

$\sqrt[4]{ \frac{1}{256} } = \frac{ \sqrt[4]{1} }{ \sqrt[4]{256} } = \frac{1}{4}$

Espero ter ajudado.

Answer 2

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$\boxed{\begin{array}{c|l}\sf256&\sf2\\\sf128&\sf2\\\sf64&\sf2\\\sf32&\sf2\\\sf16&\sf2\\\sf8&\sf2\\\sf4&\sf2\\\sf2&\sf2\\\sf1\end{array}}$

$\Large\boxed{\begin{array}{l}\sf\sqrt[\sf4]{\sf\dfrac{1}{256}}=\sqrt[\sf4]{\sf \dfrac{1}{2^8}}=\sqrt[\sf4]{\sf\bigg(\dfrac{1}{2}\bigg)^8}\\\sf=\sqrt[\sf\diagdown\!\!\!\!4]{\sf\bigg(\bigg[\dfrac{1}{2}\bigg]^2\bigg)^{\diagdown\!\!\!\!4}}=\bigg[\dfrac{1}{2}\bigg]^2=\dfrac{1}{4}\end{array}}$