Practice: Exponents

Part A: Product Rule (x^a times x^b = x^(a+b))

Directions: Simplify using the product rule.

1. x^4 times x^3 = _____

2. y^2 times y^7 = _____

3. a^5 times a = _____

4. 2^3 times 2^4 = _____

5. m^6 times m^6 = _____

6. b times b^8 = _____

Part B: Quotient Rule (x^a / x^b = x^(a-b))

Directions: Simplify using the quotient rule.

7. x^9 / x^4 = _____

8. y^12 / y^5 = _____

9. a^8 / a^8 = _____

10. 5^7 / 5^3 = _____

11. m^10 / m^2 = _____

12. z^6 / z = _____

Part C: Power Rule ((x^a)^b = x^(ab))

Directions: Simplify using the power rule.

13. (x^2)^5 = _____

14. (y^4)^3 = _____

15. (a^6)^2 = _____

16. (2^3)^4 = _____

17. (m^5)^4 = _____

18. (b^1)^10 = _____

Part D: Zero and Negative Exponents

Directions: Evaluate or simplify.

19. 8^0 = _____

20. (-5)^0 = _____

21. 2^(-4) = _____

22. 5^(-2) = _____

23. x^(-3) = _____

24. 10^(-1) = _____

Part E: Mixed Practice

Directions: Use multiple rules to simplify.

25. (x^3)^2 times x^4 = _____

26. y^8 / (y^2)^3 = _____

27. (a^4 times a^2)^3 = _____

28. (2^3)^2 / 2^4 = _____

Part F: Scientific Notation Preview

Directions: Write in standard form or scientific notation.

29. 3.5 times 10^4 = _____

30. 2.1 times 10^(-3) = _____

31. 45,000 = _____ times 10^_____

32. 0.0067 = _____ times 10^_____

Challenge: Think About It!

33. Simplify completely: (x^4 times y^3)^2 / (x^2 times y)^3

Answer: _____________

34. If 2^x = 32, what is x? _____