Question

Simplifique: √(3^4)^-3/2

Answer 1

$\sqrt{(3^4)^{- \frac{3}{2} }}$

$\sqrt{ \frac{1}{(3^4)^{ \frac{3}{2} }} }$

$\sqrt{ \frac{1}{ \sqrt{(3^4)^3} } }$

$\boxed{ \sqrt{ \frac{1}{ \sqrt{3^{12}} } } ~\to~ \frac{ \sqrt{1} }{ \sqrt[4]{3^{12}} } ~\to~ \frac{1}{3^3} ~\to~3^{-3}}$

Answer 2

$\sqrt{(3^4)^- \frac{3}{2} } = \sqrt{3^-^6} = \sqrt{( \frac{1}{3})^6 }$

$= \frac{ \sqrt{1} }{ \sqrt{3^6} } = \frac{1}{3^3} =3^-^3$

Explicação:
(3⁴)^-3/2 = 4*(-3/2) = -12/2 = -6---> então ficou 3^-6