Solve the equation below pls show your work no links pls. (9^(2) )^(-1/3)

Question

Solve the equation below pls show your work no links pls.

`(9^(2) )^(-1/3)`

Answer 1

Given :-

• 
  `(9^(2) )^(-1/3)`

To Find :-

• To solve the expression .

Solution :-

Given expression to us is ,

`(9^(2) )^(-1/3)`

We know that ,

`9 = 3^2`

So our expression becomes ,

`\{ (3^2)^2\}^{(-1)/(3)}`

And ,
`(a^m)^n =a^(mn)` . Using this ,

`(3^4)^{(-1)/(3)}`

Again using the same law ,

`3^{(-4)/(3)}`

We know that ,
`a^(-m)=(1)/(a^m)` . Therefore ,

`(3^(-4))^{(1)/(3)}`

`\\\bigg( (1)/(3^4)\bigg)^(1/3)`

`\\ \frac{1}{\sqrt[3]{3^4}}`

Simplify ,

`\frac{1}{3\sqrt[3]{3}}`

This is the simplified expression.

I hope this helps.