1. **State the problem:** Simplify the expression $(-3x)^3$. 2. **Recall the formula:** When raising a product to a power, use the rule $$(ab)^n = a^n b^n$$ where $a$ and $b$ are factors and $n$ is the exponent. 3. **Apply the rule:** Here, $a = -3$ and $b = x$, and $n = 3$, so $$(-3x)^3 = (-3)^3 \cdot x^3$$ 4. **Calculate each part:** $$(-3)^3 = -3 \times -3 \times -3 = -27$$ 5. **Combine the results:** $$(-3x)^3 = -27x^3$$ 6. **Final answer:** $$\boxed{-27x^3}$$