Here are the simplified solutions with only positive exponents:

1. $2m^2 \cdot 2m^3 = 4m^{2+3} = 4m^5$

2. $m^4 \cdot 2m^{-3} = 2m^{4+(-3)} = 2m^1 = 2m$

3. $4r^{-3} \cdot 2r^{-2} = 8r^{-3+(-2)} = 8r^{-5} = \frac{8}{r^5}$

4. $4n^4 \cdot 2n^{-3} = 8n^{4+(-3)} = 8n^1 = 8n$

5. $2k^4 \cdot 4k = 8k^{4+1} = 8k^5$

6. $2x^3y^{-3} \cdot 2x^{-1}y^3 = 4x^{3+(-1)}y^{-3+3} = 4x^2y^0 = 4x^2$

7. $2y^2 \cdot 3x = 6x y^2$

8. $4v^3 \cdot vu^2 = 4v^{3+1}u^2 = 4v^4u^2$

9. $4a^3b^2 \cdot 3a^{-4}b^{-3} = 12a^{3+(-4)}b^{2+(-3)} = 12a^{-1}b^{-1} = \frac{12}{ab}$

10. $x^2y^{-4} \cdot x^3y^2 = x^{2+3}y^{-4+2} = x^5y^{-2} = \frac{x^5}{y^2}$

Let me know if you want further explanations or additional clarifications.

Follow-Up Questions:

1. What are the general rules for adding exponents in multiplication?
2. How do you simplify expressions with negative exponents?
3. Can you explain the difference between multiplying coefficients and combining exponents?
4. What happens when a variable is raised to the zero power?
5. How do fractions simplify when using positive exponents?

Tip:

Always remember to handle coefficients and exponents separately when simplifying terms.