Section 6.1 Exponential Expressions

1. Section 6.1 Exponential Expressions Objective 1: To multiply monomials. Objective 2: To divide monomials and simplify expressions with negative exponents.

2. Objective 1 To multiply monomials

3. Exponent Review Exponent Base

4. What does it mean? It means to use 2 as a factor 5 times.

5. What does it mean?

7. Exponent Review Exponent Base

8. What does it mean?

9. What does it mean?

10. Multiplying with exponents • When you multiply, add the exponents.

11. Example 1 What’s the exponent for this x?

12. Example 1 Multiply the coefficients first.

13. Example 1

14. Example 1

15. Example 2

16. Example 2

17. Raising a power to a power • When raising a power to another power, multiply the exponents.

18. Raising a power to a power • When raising a power to another power, multiply the exponents. Take everything in parentheses and raise it to the 2nd power.

19. Raising a power to a power • When raising a power to another power, multiply the exponents. Use Distributive Property.

20. Example 3 Simplify the coefficient.

21. Example 3

22. Example 4 What’s the exponent for this x? What’s the exponent for this x?

23. Example 4 Simplify this expression first because it has an outside exponent. Take everything in parentheses and raise it to the 3rd power.

24. Example 4 Now, there are no outside exponents. We can multiply the coefficients Then multiply the x’s Then multiply the y’s

25. Example 4

26. Example 4

27. Example 5 (skip) Start outside the brackets Multiply the two outside exponents.

28. Example 5 Simplify the outside exponent. Raise everything inside the parentheses to the 6th power.

29. Example 5

30. Objective 2 To divide monomials and simplify negative exponents.

31. Dividing with exponents • When you divide, subtract the exponents.

32. Example 6 What’s the exponent for this b?

33. Example 6

34. Example 7 Raise everything in the parentheses to the 2nd power.

35. Example 7 Subtract the exponents.

36. Example 7

37. Example 8 Raise everything in the parentheses to the 3rd power.

38. Example 8 Simplify the denominator.

39. Example 8

40. Look At This

41. Look At This

42. Look At This This is another rule.

43. Zero as exponent • Anything raised to zero power equals 1.

44. Review: Whole Numbers Any whole number can be placed on top of 1.

45. Review: Whole Numbers Any whole number can be placed on top of 1.

46. Review: Whole Numbers Any whole number can be placed on top of 1.

47. Review: Whole Numbers Any whole number can be placed on top of 1.

48. Review: Whole Numbers Any whole number can be placed on top of 1.

49. Review: Whole Numbers Any whole number can be placed on top of 1.

50. Fractions There are 2 parts of a fraction.