1. **State the problem:** Simplify the expression $$-8 a^4 b (+2 a^3 b^3)$$. 2. **Recall the distributive property:** When multiplying a term by a sum, multiply the term by each addend separately: $$x(y+z) = xy + xz$$ 3. **Apply the distributive property:** $$-8 a^4 b \times 2 a^3 b^3 = -8 \times 2 \times a^4 \times a^3 \times b \times b^3$$ 4. **Multiply the coefficients:** $$-8 \times 2 = -16$$ 5. **Use the rule for multiplying powers with the same base:** $$a^m \times a^n = a^{m+n}$$ $$b^m \times b^n = b^{m+n}$$ 6. **Add the exponents:** $$a^{4+3} = a^7$$ $$b^{1+3} = b^4$$ 7. **Combine all parts:** $$-16 a^7 b^4$$ **Final answer:** $$-16 a^7 b^4$$