Given :-
- [tex](9^{2} )^{-1/3}[/tex]
To Find :-
- To solve the expression .
Solution :-
Given expression to us is ,
[tex](9^{2} )^{-1/3}[/tex]
We know that ,
[tex] 9 = 3^2[/tex]
So our expression becomes ,
[tex]\{ (3^2)^2\}^{\frac{-1}{3}}[/tex]
And , [tex] (a^m)^n =a^{mn}[/tex] . Using this ,
[tex] (3^4)^{\frac{-1}{3}}[/tex]
Again using the same law ,
[tex] 3^{\frac{-4}{3}}[/tex]
We know that , [tex] a^{-m}=\frac{1}{a^m}[/tex] . Therefore ,
[tex] (3^{-4})^{\frac{1}{3}}[/tex]
[tex]\\\bigg( \dfrac{1}{3^4}\bigg)^{1/3}[/tex]
[tex]\\ \dfrac{1}{\sqrt[3]{3^4}}[/tex]
Simplify ,
[tex] \dfrac{1}{3\sqrt[3]{3}}[/tex]
This is the simplified expression.
I hope this helps.
