1. **State the problem:** Simplify the expression $$(5a^3 b^2)(-2a^{-2} b) - 3 + (-5a^8 b^9)(-6 - 2)$$. 2. **Use the laws of exponents and multiplication:** - When multiplying powers with the same base, add the exponents: $$a^m \cdot a^n = a^{m+n}$$. - Multiply coefficients normally. - Simplify inside parentheses first. 3. **Simplify each part:** - First part: $$(5a^3 b^2)(-2a^{-2} b) = 5 \times -2 \times a^{3 + (-2)} \times b^{2 + 1} = -10a^{1}b^{3} = -10ab^{3}$$. 4. **Simplify the second part inside the parentheses:** $$-6 - 2 = -8$$. 5. **Simplify the second big term:** $$(-5a^8 b^9)(-8) = (-5) \times (-8) \times a^8 \times b^9 = 40a^8 b^9$$. 6. **Combine all parts:** $$-10ab^{3} - 3 + 40a^{8}b^{9}$$. 7. **Final simplified expression:** $$\boxed{-10ab^{3} - 3 + 40a^{8}b^{9}}$$.