https://file.aiquickdraw.com/mathbot/file/1729866965620pa2ji5ra.jpg

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

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### **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

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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!

Simplify the following expressions in the image provided.

Learn how to simplify algebraic expressions involving exponents by applying the laws of exponents. This exercise is suitable for students in grades 8 to 10 and covers key exponent rules, including powers of powers, multiplying powers with the same base, and more.

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