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Division of Powers Practice

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Division of Powers Practice

Division of Powers Practice

Mathematical powers and indices illustration

📚 Part 1: Understanding the Law of Indices for Division

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

am ÷ 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 am ÷ an = am-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

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