Question

Ayuda porfavor
es para hoy

Answer 1

Respuesta:

Propiedad de la potencia y radicación.

Explicación paso a paso:

 $\sqrt[3]{729}~=~\sqrt[3]{9^3}~=~9$

 $\sqrt[3]{\cfrac{8}{27}}~=~\cfrac{~\sqrt[3]{8}~}{\sqrt[3]{27}}~=~\cfrac{~\sqrt[3]{2^3}}{\sqrt[3]{3^3}~}~=~\cfrac{~2~}{3}$

 

$\sqrt[5]{\cfrac{243}{3125}}~=~\cfrac{~\sqrt[5]{243}~}{\sqrt[5]{3125}}~=~\cfrac{~\sqrt[5]{3^5}}{\sqrt[5]{5^5}~}~=~\cfrac{~3~}{5}$

 $\sqrt[4]{\cfrac{405}{80}}~=~\cfrac{~\sqrt[4]{405}~}{\sqrt[4]{80}}~=~\cfrac{~\sqrt[4]{3^4*5}}{\sqrt[4]{2^4*5}~}~=~\cfrac{~\sqrt[4]{3^4}*\sqrt[4]{5}}{\sqrt[4]{2^4}*\sqrt[4]{5}~}~=~\cfrac{3*\sqrt[4]{5}}{2*\sqrt[4]{5}~}~=~\cfrac{3}{2}$

 $\sqrt[4]{\cfrac{32}{162}}~=~\cfrac{~\sqrt[4]{32}~}{\sqrt[4]{162}}~=~\cfrac{~\sqrt[4]{2^4*2}}{\sqrt[4]{3^4*2}~}~=~\cfrac{~\sqrt[4]{2^4}*\sqrt[4]{2}}{\sqrt[4]{3^4}*\sqrt[4]{2}~}~=~\cfrac{2*\sqrt[4]{2}}{3*\sqrt[4]{2}~}~=~\cfrac{2}{3}$