1. **State the problem:** Find the product and simplify the expression $$(9m^4)(-8m^3)$$. 2. **Recall the multiplication rules:** When multiplying coefficients (numbers), multiply them directly. When multiplying powers with the same base, add the exponents: $$a^m \times a^n = a^{m+n}$$. 3. **Multiply the coefficients:** $$9 \times (-8) = -72$$. 4. **Multiply the powers of $m$:** $$m^4 \times m^3 = m^{4+3} = m^7$$. 5. **Combine the results:** $$-72m^7$$. 6. **Final answer:** The simplified product is $$\boxed{-72m^7}$$.