Question

a raiz quadrada do resultado da razão (3²)-³ : (9²)-³é:

Answer 1

$(3^2)^{-3}\div(9^2)^{-3}= \\ \\ 3^{-6} \div9^{-6}= \\ \\ 3^{6}\div(3^2)^{-6}= \\ \\ 3^{-6}\div3^{-12}= \\ aplica ~~a~~propriedade~~de~~divis\tilde{a}o~~de~~pot\hat{e}ncia~~de~~mesma~~base \\ \\ 3^{-6-(-12)}=3^{-6+12}=3^6 \\ \\ \sqrt{3^6} =3^3=27$

Answer 2

$\sqrt{ \dfrac{(3^2)^-^3 }{(9^2)^-^3} } \\ \\ \sqrt{ \dfrac{3^{2 \cdot (-3)} }{9^{2 \cdot (-3)} }} \\ \\ \sqrt{ \dfrac{3^{-6}}{9^{-6}} } \\ \\ \sqrt{ \dfrac{3^{-6}}{(3^{2})^{-6}} } \\ \\ \sqrt{ \dfrac{3^{-6}}{3^{2 \cdot (-6)}} } \\ \\ \sqrt{ \dfrac{3^{-6}}{3^{-12}} } \\ \\ \sqrt{3^{-6-(-12)}} \\ \\ \sqrt{3^{-6+12}} \\ \\ \sqrt{3^6} \\ \\ \sqrt{3^2 \cdot 3^2 \cdot 3^2} \\ \\ 3 \cdot 3 \cdot 3 \\ \\ \boxed{27}$



Bons estudos!