Question

Quanto é raiz de 2 elevado a -1/2? 

Answer 1

Olá,

use as propriedades da exponenciação:

$a^{-m}~\to~ \dfrac{1}{a^m}\\\\ \sqrt[n]{a^m}~\to~a^{ \tfrac{m}{n}}\\\\ (a^m)^n~\to~a^{m\cdot n}~\to~a^{mn}$

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$( \sqrt{2})^{- \tfrac{1}{2}}= \dfrac{1}{ \sqrt{2}^{ \tfrac{1}{2} } }\\\\\\ ( \sqrt{2})^{- \tfrac{1}{2} }= \dfrac{1}{2^{ \tfrac{1}{2}\cdot \tfrac{1}{2} }}\\\\\\ ( \sqrt{2} )^{- \tfrac{1}{2}}= \dfrac{1}{2^{ \tfrac{1}{4} }}\\\\\\ ( \sqrt{2})^{- \tfrac{1}{2}}= \dfrac{1}{ \sqrt[4]{2} }= \dfrac{1 \cdot\sqrt[4]{2} }{ \sqrt[4]{2}\cdot \sqrt[4]{2} }=\Large\boxed{\boxed{ \dfrac{ \sqrt[4]{2} }{2}}}.\\.$

Tenha ótimos estudos =))