Question

Solve the equation below pls show your work no links pls. %7D" id="TexFormula1" title="(9^{2} )^{-1/3}" alt="(9^{2} )^{-1/3}" align="absmiddle" class="latex-formula">

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 ,

$\{ (3^2)^2\}^{\frac{-1}{3}}$

And , $(a^m)^n =a^{mn}$ . Using this ,

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

Again using the same law ,

$3^{\frac{-4}{3}}$

We know that , $a^{-m}=\frac{1}{a^m}$ . Therefore ,

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

$\\\bigg( \dfrac{1}{3^4}\bigg)^{1/3}$

$\\ \dfrac{1}{\sqrt[3]{3^4}}$

Simplify ,

$\dfrac{1}{3\sqrt[3]{3}}$

This is the simplified expression.

I hope this helps.