1. **State the problem:** Evaluate the expression $7^3 - 3(-4)^3$ and verify if the handwritten result $535$ is correct. 2. **Recall the formulas and rules:** - Cube of a number: $a^3 = a \times a \times a$ - Multiplication and subtraction follow standard arithmetic rules. - Remember that $(-4)^3 = -4 \times -4 \times -4$. 3. **Calculate each term:** - Calculate $7^3$: $$7^3 = 7 \times 7 \times 7 = 343$$ - Calculate $(-4)^3$: $$(-4)^3 = -4 \times -4 \times -4 = -64$$ 4. **Multiply $-3$ by $(-4)^3$:** $$-3 \times (-64) = 192$$ 5. **Combine the terms:** $$7^3 - 3(-4)^3 = 343 + 192 = 535$$ 6. **Conclusion:** The handwritten result $535$ is correct.