1. **State the problem:** Evaluate the expression $$-7^3 - 3(-4)^3$$. 2. **Recall the rules:** - Exponentiation is done before multiplication and subtraction. - Negative signs without parentheses apply after exponentiation. - For example, $$-7^3 = -(7^3)$$. 3. **Calculate each term:** - Calculate $$7^3 = 7 \times 7 \times 7 = 343$$, so $$-7^3 = -343$$. - Calculate $$(-4)^3 = (-4) \times (-4) \times (-4) = -64$$. - Multiply by -3: $$-3 \times (-64) = 192$$. 4. **Combine the results:** $$-343 + 192 = -151$$. 5. **Final answer:** $$\boxed{-151}$$. **Note:** The user's calculation of 343 instead of -343 for $$-7^3$$ is incorrect, leading to a wrong final answer.