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Let's go through the questions shown on the board, which are related to the properties of exponents:

### L1: Evaluate
1. **a) \( 20^0 \)**
   - Any non-zero number raised to the power of 0 is 1.
   - \( 20^0 = 1 \)

2. **b) \( 5^3 \times 5^4 \)**
   - Use the property \( a^m \times a^n = a^{m+n} \).
   - \( 5^3 \times 5^4 = 5^{3+4} = 5^7 \)

3. **c) \( \frac{5^8}{5^7} \)**
   - Use the property \( \frac{a^m}{a^n} = a^{m-n} \).
   - \( \frac{5^8}{5^7} = 5^{8-7} = 5^1 = 5 \)

4. **d) \( (5^2)^3 \)**
   - Use the property \( (a^m)^n = a^{m \times n} \).
   - \( (5^2)^3 = 5^{2 \times 3} = 5^6 \)

### L2: Evaluate
1. **a) \( 5^{-4} \)**
   - Use the property \( a^{-n} = \frac{1}{a^n} \).
   - \( 5^{-4} = \frac{1}{5^4} \)

2. **b) \( \frac{1}{3^{-5}} \)**
   - Simplify the negative exponent using \( \frac{1}{a^{-n}} = a^n \).
   - \( \frac{1}{3^{-5}} = 3^5 \)

3. **c) \( \frac{4^{-8}}{4^{-5}} \)**
   - Use \( \frac{a^m}{a^n} = a^{m-n} \).
   - \( \frac{4^{-8}}{4^{-5}} = 4^{-8 - (-5)} = 4^{-3} = \frac{1}{4^3} \)

4. **d) \( (4^{-2})^{-5} \)**
   - Use \( (a^m)^n = a^{m \times n} \).
   - \( (4^{-2})^{-5} = 4^{(-2) \times (-5)} = 4^{10} \)

### Extension: 
Evaluate \( \frac{3^{-9}}{3^{-6}} \times (3^2)^5 \)

1. Simplify \( \frac{3^{-9}}{3^{-6}} \) using \( \frac{a^m}{a^n} = a^{m-n} \):
   - \( \frac{3^{-9}}{3^{-6}} = 3^{-9 - (-6)} = 3^{-3} \)

2. Simplify \( (3^2)^5 \) using \( (a^m)^n = a^{m \times n} \):
   - \( (3^2)^5 = 3^{2 \times 5} = 3^{10} \)

3. Multiply the results:
   - \( 3^{-3} \times 3^{10} = 3^{-3 + 10} = 3^7 \)

Would you like further details or have any questions?

### 5 Related Questions:
1. What is the general rule for multiplying powers with the same base?
2. How do you handle negative exponents in fractional form?
3. How does raising a power to another power work?
4. What is the rule for dividing powers with the same base?
5. How do you simplify an expression with a zero exponent?

### Tip:
When dealing with exponents, always remember to apply the correct exponent rule based on the operation (multiplication, division, or power to power).

Evaluate using the properties of exponents: L1) a) 20^0, b) 5^3 × 5^4, c) 5^8 / 5^7, d) (5^2)^3; L2) a) 5^-4, b) 1 / 3^-5, c) 4^-8 / 4^-5, d) (4^-2)^-5; Extension: Evaluate (3^-9 / 3^-6) × (3^2)^5

Learn how to evaluate expressions involving exponent properties such as multiplication and division of powers, negative exponents, and raising a power to a power. This problem covers key exponent rules for students in Grades 8-10.

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