If $f(x) = x^2$ for each $x\in (-\infty,\infty)$, then $\large \dfrac{f\left(f\left(f(x)\right)\right)}{f(x)}$ is equal to _______.

1. $f(x)$
2. $(f(x))^2$
3. $(f(x))^3$
4. $(f(x))^4$

Given that, $f(x) = x^{2}.$
Now, $f\left(f\left(f(x)\right)\right) = f\left(f\left(x^{2}\right)\right) = f\left(x^{4}\right) = x^{8}$
$\therefore \dfrac{f\left(f\left(f(x)\right)\right) }{f(x)} = \dfrac{x^{8}}{x^{2}} = x^{6} = (x^{2})^{3} = (f(x))^{3}.$
So, the correct answer is $(C).$