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Exponents

Exponents. Standard:. Exponent:. Tells how many times a base is used as a factor. 2 ³ = 2 ∙ 2 ∙ 2. Exponent. Base. Power. You try!. Common Exponents. Squared: anything to the second power Example: 9² is 9 squared Cubed: anything to the third power

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Exponents

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  1. Exponents Standard:

  2. Exponent: Tells how many times a base is used as a factor. 2³ = 2 ∙ 2 ∙ 2 Exponent Base Power

  3. You try!

  4. Common Exponents Squared: anything to the second power Example: 9² is 9 squared Cubed: anything to the third power Example: 10³ is 10 cubed

  5. Zero Power: anything to the zero power is ONE! Example: 8⁰ = 1 (-24)⁰ = 1 2,500,050⁰ = 1

  6. Problem of the DAY! What is the value of 7⁰? • 1 • 0 • 7 • 1/7 Anything to the Power of Zero is ONE!

  7. Remember! The exponent tells you how many times you will multiply the same number by itself! Even when it is negative! For example: (-5)³ = (-5) ∙ (-5) ∙ (-5) = 125

  8. Negative numbers When the negative is inside the parenthesis, then it is the same negative number multiplied by itself When it is outside, you add the negative at the end!

  9. You try it!

  10. This time it’s different!

  11. Example: Write using exponents: a ∙ b ∙ b ∙ b ∙ a • a b • a b • a b • aabbb 3 2 2 3 2 2

  12. And again! x ∙ y ∙ x ∙ x ∙ x∙ x ∙ y ∙ x • x y • x y • 6x2y • x y 6 2 5 2 5 2

  13. And again! Simplify (ab)³ using exponents. • ababab • a³b³ • 3a3b • a²b²

  14. Negative Exponents 1 a = -n n a Example:

  15. Example 2

  16. You try it!

  17. Problem of the Day (Thursday) 4 What is (-12) ? • 20736 • -20736 • 48 • -48

  18. Exponents – Review!

  19. Review 2

  20. Review 3

  21. Review 4 -2 What is 5 ? a. -25 b. 25 c. 1 d. 1 25 -25

  22. Review 5 What is 3x ∙ 3x ∙ 3x? • 3x³ • 27x • 9x • 27x³

  23. Multiplying Exponents To multiply numbers or variables with the same base, add the exponents Example: 3³ ∙ 3² = 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 = 3 = 3 = 243 (3+2) 5

  24. You try!

  25. Try again!

  26. And again!

  27. Dividing Exponents When dividing exponents, you subtract! 7 3 3² (7-2) 3 = 3 5

  28. Example 2

  29. You try it!

  30. And again! 99 Solve (-7) (-7) 98 • -7 • 1 • 7 • 7 97

  31. And again! 4 Solve w w 6 • w² • -2w • w • 1 2 w²

  32. Exponents Raised to a Power Example: (2⁵)² *Multiply the exponents

  33. How to do it on your calculator!

  34. Problem of the Day (Friday) 8 Write x ∙ x using a single exponent • x • x • x • x 12 8 7 9

  35. Problem of the Day (Tuesday) Write the number 124,000,000 in scientific notation. • 1.24 x 10 • 124 x 10 • 1.24 x 10 • 12.4 x 10 8 6 6 7

  36. Problem of the Day (Tuesday) Write the following using a positive exponent: 6 ∙ 6 a. 6³ b. 1_ 6³ c. 1_ 6 d. 6 2 -5 5 5

  37. Review

  38. Review

  39. Scientific Notation

  40. Why do we use it? Scientific notation is a way of writing extremely small or large numbers in a way that is easier.

  41. Scientific Notation: A single digit (greater than or equal to 1 but less than 10) multiplied by a power of ten Example: 37,000,000 in scientific notation 3.7 x 10 7

  42. The other way around 1.55 x 10 in standard form 1,550,000 6

  43. Write the number 124,000,000 in scientific notation. • 1.24 x 10 • 124 x 10 • 1.24 x 10 • 12.4 x 10 8 6 6 7

  44. Another example!

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