I'll help you simplify these expressions step-by-step. Below are the solutions:

1 to 10

1. (w²)⁵ = w¹⁰
2. (3²)² = 3⁴ = 81
3. (z⁴)⁴ = z¹⁶
4. (2w²)² = 2² * w⁴ = 4w⁴
5. (xy²)³ = x³ * y⁶
6. (3a⁴b²c³)³ = 3³ * a¹² * b⁶ * c⁹ = 27a¹²b⁶c⁹
7. (3m⁴n⁵)³ = 3³ * m¹² * n¹⁵ = 27m¹²n¹⁵
8. (6x³y⁴)³ = 6³ * x⁹ * y¹² = 216x⁹y¹²
9. (3a⁵b⁷)⁴ = 3⁴ * a²⁰ * b²⁸ = 81a²⁰b²⁸
10. (z³w³)⁴ = z¹² * w¹²

11 to 20

11. (m²n⁶)⁴ = m⁸ * n²⁴
12. (x³y⁵)⁵ = x¹⁵ * y²⁵
13. (2pq⁷r³)⁵ = 2⁵ * p⁵ * q³⁵ * r¹⁵ = 32p⁵q³⁵r¹⁵
14. (2x²y³)⁴ = 2⁴ * x⁸ * y¹² = 16x⁸y¹²
15. (3xy²z³)⁵ = 3⁵ * x⁵ * y¹⁰ * z¹⁵ = 243x⁵y¹⁰z¹⁵
16. (3³y²)⁴ = 3¹² * y⁸ = 531441y⁸
17. (mn)²(2m²n)³ = (m²n²) * (8m⁶n³) = 8m⁸n⁵
18. (ax³)²(ax⁴)³ = a²x⁶ * a³x¹² = a⁵x¹⁸
19. (ab²)⁴(a⁴b²)³ = a⁴b⁸ * a¹²b⁶ = a¹⁶b¹⁴
20. (5a²xy³)(b³y⁴)³ = 5a²xy³ * b⁹y¹² = 5a²b⁹xy¹⁵

If you have any specific question about the steps or need clarifications, feel free to ask!

Follow-up questions:

1. What rules are applied when simplifying exponents?
2. How do you handle negative exponents or zero exponents in these kinds of problems?
3. Why do we multiply exponents when raising a power to another power?
4. Can you explain product rules for exponents in more detail?
5. How does distribution work when dealing with coefficients and variables together?

Tip: When raising a power to another power, always multiply the exponents!