Index Laws: Multiplying Powers
Name: _________________________
Date: _________________________
Remember the Rule:
When multiplying powers with the same base: am × an = am+n
Example: 2³ × 2⁵ = 2³⁺⁵ = 2⁸
Part A: Simplify each expression
1. 3² × 3⁴ = ______________
2. 5³ × 5² = ______________
3. 7⁴ × 7³ = ______________
4. 2⁵ × 2⁶ = ______________
5. 10² × 10⁷ = ______________
6. 4³ × 4 = ______________
7. 6⁵ × 6⁴ = ______________
8. 9² × 9³ = ______________
Part B: Simplify using algebra
9. x³ × x⁵ = ______________
10. y⁴ × y² = ______________
11. a⁶ × a = ______________
12. m² × m⁸ = ______________
13. p⁷ × p³ = ______________
14. k × k⁹ = ______________
15. b⁵ × b⁵ = ______________
16. n⁴ × n⁴ = ______________
Part C: More complex expressions
17. 2³ × 2² × 2⁴ = ______________
18. 5² × 5 × 5³ = ______________
19. x² × x³ × x⁴ = ______________
20. a × a⁵ × a² = ______________
Part D: Challenge Questions
21. If 3ˣ × 3⁴ = 3⁹, what is the value of x? x = ______________
22. If y⁵ × ya = y¹², what is the value of a? a = ______________
23. Simplify: 2² × 3³ × 2⁴ × 3² = ______________
24. Simplify: m³ × n² × m⁵ × n⁴ = ______________