📚 Part 1: Understanding the Law of Indices for Division

1. Complete the rule for dividing powers with the same base:

a^m ÷ aⁿ = a^_______

2. Circle the correct answer for 5⁷ ÷ 5³:

5⁴

5¹⁰

5²¹

1⁴

3. Which of these expressions can be simplified using the division law of indices? (Check all that apply):

x⁸ ÷ x³

7⁵ ÷ 3²

2⁹ ÷ 2⁴

a⁶ ÷ b⁶

🔢 Part 2: Basic Division of Powers

4. Simplify these expressions. Show your working:

a) 3⁶ ÷ 3² = ___________

b) 10⁸ ÷ 10⁵ = ___________

c) 4⁹ ÷ 4⁴ = ___________

d) 2¹² ÷ 2⁷ = ___________

📐 Part 3: Algebraic Expressions

5. Simplify these algebraic expressions:

a) x⁹ ÷ x⁴ = ___________

b) y¹⁵ ÷ y⁸ = ___________

c) a¹¹ ÷ a³ = ___________

d) m²⁰ ÷ m¹² = ___________

🎯 Part 4: Special Cases and Order of Operations (GEMA)

6. What happens when the powers are equal? Simplify:

a) 5⁶ ÷ 5⁶ = ___________

b) x⁴ ÷ x⁴ = ___________

7. Use GEMA (order of operations) to evaluate these expressions:

a) 2⁵ ÷ 2² + 3² = ___________

b) (6⁴ ÷ 6²) × 2 = ___________

🔍 Part 5: Error Analysis and Problem Solving

8. Sam simplified 7⁸ ÷ 7³ and got 1⁵. Explain what Sam did wrong and show the correct answer:

9. Match each expression with its simplified form:

1. 8⁷ ÷ 8³

2. x¹² ÷ x⁵

3. 3¹⁰ ÷ 3¹⁰

4. y⁹ ÷ y²

A. x⁷

B. 8⁴

C. 1

D. y⁷

10. Challenge: Simplify this more complex expression:

(a⁸ ÷ a³) ÷ a² = ___________

💭 Part 6: Reflection

11. In your own words, explain why a^m ÷ aⁿ = a^m-n works:

12. Rate your confidence with dividing powers (circle one):

Very confident - I can teach someone else!

Confident - I understand most problems

Getting there - I need a bit more practice

Need help - I'm still confused about some parts

Division of Powers Practice

Division of Powers Practice

📚 Part 1: Understanding the Law of Indices for Division

🔢 Part 2: Basic Division of Powers

📐 Part 3: Algebraic Expressions

🎯 Part 4: Special Cases and Order of Operations (GEMA)

🔍 Part 5: Error Analysis and Problem Solving

💭 Part 6: Reflection

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