Index Laws: Dividing Powers

Name: _____________________________

Date: _____________________________

Remember the Division Law:

a^m ÷ aⁿ = a^m−n

When dividing powers with the same base, subtract the exponents.

Section A: Simplify each expression

1. 5⁸ ÷ 5³ = __________________

2. 7⁹ ÷ 7⁴ = __________________

3. 2¹² ÷ 2⁵ = __________________

4. 3¹⁰ ÷ 3⁶ = __________________

5. 6⁷ ÷ 6² = __________________

6. 4¹¹ ÷ 4⁸ = __________________

7. 10¹⁵ ÷ 10⁹ = __________________

8. 8⁶ ÷ 8¹ = __________________

9. x⁹ ÷ x⁴ = __________________

10. a¹¹ ÷ a⁷ = __________________

11. m⁸ ÷ m³ = __________________

12. p¹⁴ ÷ p⁶ = __________________

13. y²⁰ ÷ y¹⁵ = __________________

14. b¹³ ÷ b⁹ = __________________

15. c⁷ ÷ c⁷ = __________________

16. 9¹⁰ ÷ 9¹⁰ = __________________

17. n⁵ ÷ n = __________________

18. 12⁶ ÷ 12² = __________________

19. t¹⁰⁰ ÷ t⁹⁵ = __________________

20. k¹⁸ ÷ k¹² = __________________

21. If 3¹² ÷ 3ⁿ = 3⁵, then n = __________________

22. If x¹⁵ ÷ x⁸ = x^k, then k = __________________

23. Simplify: (a¹⁰ ÷ a³) ÷ a² = __________________