1. **State the problem:** Identify which expressions are equivalent to $6^3 \cdot 3^3$. 2. **Recall the property of exponents:** For any positive numbers $a$ and $b$, and exponent $n$, we have: $$ (a \cdot b)^n = a^n \cdot b^n $$ 3. **Apply the property:** $$ 6^3 \cdot 3^3 = (6 \cdot 3)^3 = 18^3 $$ 4. **Check each expression:** - $18^3$ is exactly $(6 \cdot 3)^3$, so it is equivalent. - $18^9$ is $18^{3 \times 3}$, which is not equivalent to $18^3$. - $(18^1)^3 = 18^3$, so it is equivalent. - $\frac{1}{18^3} = 18^{-3}$, which is not equivalent. **Final answer:** The expressions equivalent to $6^3 \cdot 3^3$ are $18^3$ and $(18^1)^3$.