Given equation.
\(\displaystyle{4}{x}^{{3}}={324}\)

Divide both sides by 4. \(\displaystyle{x}^{{3}}={81}\)

Now we need to get rid of that cube so we'll take the cube root of both sides. \(\displaystyle{3}\sqrt{{x}}^{{3}}={3}\sqrt{{x}}^{{81}}\) x=3sqrtx^81

Now your answer will depend on your class and what your teacher expects for this assignment. If you teacher just wants a number then you can plug this into your calculator to get x=4.3267487…

However, if your teacher expects you to simplify the expression but leave it as an expression then we're going to need to factor that 81. So let's think about things that multiply to be 81. 9×9 works. But each of those 9's can be factored further to 3×3. But there's nothing smaller than a three that you can multiply together to get three. So that's it. Thus

\(\displaystyle{81}={3}×{3}×{3}×{3}\)

So taking the cube root we get

\(\displaystyle{x}={3}√{81}={3}×{3}×{3}×{3}={3}\cdot{3}√{3}\)

Divide both sides by 4. \(\displaystyle{x}^{{3}}={81}\)

Now we need to get rid of that cube so we'll take the cube root of both sides. \(\displaystyle{3}\sqrt{{x}}^{{3}}={3}\sqrt{{x}}^{{81}}\) x=3sqrtx^81

Now your answer will depend on your class and what your teacher expects for this assignment. If you teacher just wants a number then you can plug this into your calculator to get x=4.3267487…

However, if your teacher expects you to simplify the expression but leave it as an expression then we're going to need to factor that 81. So let's think about things that multiply to be 81. 9×9 works. But each of those 9's can be factored further to 3×3. But there's nothing smaller than a three that you can multiply together to get three. So that's it. Thus

\(\displaystyle{81}={3}×{3}×{3}×{3}\)

So taking the cube root we get

\(\displaystyle{x}={3}√{81}={3}×{3}×{3}×{3}={3}\cdot{3}√{3}\)