We can simplify this expression by using the rule that states \(\frac{a^m}{a^n}=a^{m-n}\) for any non-zero real number a and integers m and n. Applying this rule, we get:
\[\frac{3x^3}{(3x)^3} = \frac{3x^3}{27x^3} = \frac{1}{9}\]
Therefore, the answer is \(\frac{1}{9}\).