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Multiplying Indices Practice

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Multiplying Indices Practice

Multiplying Indices Practice

Mathematical indices illustration

📚 Part 1: Understanding the Multiplication Law

1. Complete the rule for multiplying indices with the same base:

am × an = a_______

2. Circle the correct answer. When multiplying powers with the same base, we:

Add the indices

Multiply the indices

Subtract the indices

Divide the indices

3. Explain why 2³ × 2⁴ = 2⁷ using repeated multiplication:

🔢 Part 2: Numerical Examples

4. Simplify these expressions using the multiplication law:

a) 3² × 3⁵ = ___________

b) 5³ × 5² = ___________

c) 4⁴ × 4³ = ___________

d) 10³ × 10⁴ = ___________

5. Check all expressions that are correctly simplified:

2³ × 2⁴ = 2⁷

6² × 6³ = 6⁶

7¹ × 7⁵ = 7⁶

9² × 9² = 9⁸

📐 Part 3: Algebraic Expressions

6. Simplify these algebraic expressions:

a) x⁴ × x⁶ = ___________

b) y² × y⁷ = ___________

c) a³ × a⁵ = ___________

d) m¹ × m⁸ = ___________

7. More challenging expressions:

a) (2a)³ × (2a)² = ___________

b) (3x)² × (3x)⁴ = ___________

⚠️ Part 4: Common Mistakes

8. Circle the INCORRECT simplification:

x³ × x² = x⁵

4² × 4³ = 4⁶

y⁴ × y¹ = y⁵

5³ × 5² = 5⁵

9. Explain what is wrong with this working: 2³ × 2⁴ = 2¹²
10. Match each expression with its correct simplified form:
1. x² × x³
2. 3⁴ × 3¹
3. y⁶ × y²
4. 2² × 2⁵
A. 2⁷
B. x⁵
C. y⁸
D. 3⁵

🚀 Part 5: Extension Problems

11. Scientific notation problems:

a) (10³) × (10⁴) = ___________

b) (10²) × (10⁶) = ___________

12. Challenge: Simplify these expressions with multiple terms:

a) a² × a³ × a⁴ = ___________

b) x¹ × x² × x³ × x⁴ = ___________

13. Create your own example of multiplying indices and solve it:

🎯 Part 6: Exit Ticket

14. Final check - Simplify: 4³ × 4⁵ = ___________
15. In your own words, explain the multiplication law of indices:

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