Exponent Rules

1. Exponent Rules

2. The exponent indicates the number of times the base is used as a factor. EXPONENT 5 2 BASE POWER = 2x2x2x2x2 =32

3. Zero Exponents Any number raised to the zero power equals one! Ex) Ex) Ex) = 1 = 1 = 1 Another important note: All numbers or variables have an exponent of ONE. So, x is the same as and 3 is the same as and so on.

4. Placement of the Negative • Placement of the negative is important! • For example, when simplifying an expression you have to follow the order of operations • means square 2 and then mult. by -1. • But means multiply • -2 by-2

5. Your Turn = -3 = -16 = 16 (-1)4 -14 = -1 = 1 = -1 = 1

6. Product Rule for Exponents Think about it. Say you’re multiplying x3·x2. X3 means x·x·x and x2 means x·x. So x·x·x·x·x = x5. Add the exponents to get the correct power. When multiplying numbers or variables with like bases ADD the exponents.

7. Example 1.

8. Example 2. You try it !!!

9. Example 3 You Try It!

10. Example 4 NOTE: Multiply the coefficients and add the exponents on the like bases. Leave the bases the same.

11. Example 5

12. Example 6

13. Example 7

14. Power of a Power • To Find the Power of a Power, Multiply the EXPONENTS. • For Instance: (am)n = am*n Be sure to multiply the exponent outside the parentheses by all of the exponents inside the parentheses!

15. Example 1 (x3)4 =x12

16. Example 2 (x2)3 x6

17. Example 3

18. 52m6 Example 4 25m6 or

19. Example 5

20. Answer or

21. Quotient Rule for Exponents We can divide two quantities with exponents if they have the same base. To divide two quantities with the same base, subtract the exponents and keep the base thesame.

22. Example 1

23. Example 2 You Try It!

24. Example 3 You Try It! or 32

25. Example 4 NOTE: Simplify the fraction part and subtract the exponents.

26. ANSWER or

27. Example 5 NOTE: Simplify the fraction part and subtract the exponents.

28. Negative Powers • Let’s define a number with a negative exponent  to be the reciprocal of that power with a positive exponent. So, to simplify an expression with a negative exponent, take the reciprocal, and make the exponent positive. • For Instance:

29. In other words, move the factor with the negative exponent to the other side of the fraction bar and make the exponent positive. • So, if a factor with a negative exponent is in the numerator, move it to the denominator and make the exponent positive, and vice versa.

30. Example 1

31. ANSWER

32. Example 2

33. ANSWER or

34. Example 3 Hint: the negative exponent only applies to the number or variable it is directly beside

35. ANSWER

36. Example 4

37. Exponent Rules

38. The exponent indicates the number of times the _____ is used as a _______. __________ 5 2 _________ _________ = _______________

39. Zero Exponents Any number raised to the zero power equals one! Ex) Ex) Ex) = __ = __ = __ Another important note: All numbers or variables have an exponent of ONE. So, x is the same as and 3 is the same as and so on.

40. Placement of the Negative • Placement of the negative is important! • For example, when simplifying an expression you have to follow the order of operations • means square 2 and then mult. by -1. • But means multiply -2 by -2

41. Your Turn (-1)4 -14

42. Product Rule for Exponents Think about it. Say you’re multiplying x3·x2. X3 means x·x·x and x2 means x·x. So x·x·x·x·x = x5. Add the exponents to get the correct power. When multiplying numbers or variables with like bases _____ the exponents.

43. Example 1.

44. Example 2. You try it !!!

45. Example 3 You Try It! Remember to keep the base the same.

46. Example 4 NOTE: Multiply the coefficients and add the exponents on the like bases. Leave the base the same.

47. Example 5 You Try It!

48. Example 6

49. Example 7

50. Power of a Power • To Find the Power of a Power, ________ the EXPONENTS. • For Instance: (am)n = am*n Be sure to multiply the exponent outside the parentheses by all of the exponents inside the parentheses!