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Section 6.1 Exponential Expressions

Learn how to multiply and divide monomials and simplify expressions with negative exponents. Explore rules for raising powers to powers and the zero exponent rule.

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Section 6.1 Exponential Expressions

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  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?

  6. Exponent Review Exponent Base

  7. What does it mean?

  8. What does it mean?

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

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

  11. Example 1 Multiply the coefficients first.

  12. Example 1

  13. Example 1

  14. Example 2

  15. Example 2

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

  17. 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.

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

  19. Example 3 Simplify the coefficient.

  20. Example 3

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

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

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

  24. Example 4

  25. Example 4

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

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

  28. Example 5

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

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

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

  32. Example 6

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

  34. Example 7 Subtract the exponents.

  35. Example 7

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

  37. Example 8 Simplify the denominator.

  38. Example 8

  39. Look At This

  40. Look At This

  41. Look At This This is another rule.

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

  43. Review: Whole Numbers Any whole number can be placed on top of 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. Fractions There are 2 parts of a fraction.

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