1. **State the problem:** Simplify the expression $$(uv^3)(-2u^3vw^4) - 3$$ and write the answer using only positive exponents. 2. **Use the distributive property and laws of exponents:** $$(uv^3)(-2u^3vw^4) = u \cdot v^3 \cdot (-2) \cdot u^3 \cdot v \cdot w^4$$ 3. **Group like bases and multiply coefficients:** $$= -2 \cdot u^{1+3} \cdot v^{3+1} \cdot w^4 = -2u^4v^4w^4$$ 4. **Rewrite the entire expression:** $$-2u^4v^4w^4 - 3$$ 5. **Final answer:** $$\boxed{-2u^4v^4w^4 - 3}$$ This expression is simplified with only positive exponents and cannot be combined further because the terms are not like terms.