1. 1 Introductory Algebra Exponents & Scientific Notation

2. 2 Exponents & Scientific Notation Integer Exponents Scientific Notation Power Rules

3. 3 Integral Exponents & Scientific Notation

4. 4 Positive Integral Exponents

5. 5 Negative Integral Exponents

6. 6 If a is any nonzero real number and n is a positive integer, then a -n = 1/a n. (Note that a negative exponent is not the same or related to a negative number.)

7. 7 Negative Integral Exponents If a is any nonzero real number and n is a positive integer, then a -n = 1/a n. (Note that a negative exponent is not the same or related to a negative number.)

8. 8 Negative Integral Exponents If a is any nonzero real number and n is a positive integer, then a -n = 1/a n. (Note that a negative exponent is not the same or related to a negative number.)

9. 9 Negative Integral Exponents If a is any nonzero real number and n is a positive integer, then a -n = 1/a n. (Note that a negative exponent is not the same or related to a negative number.)

10. 10 Product Rule for Exponents

11. 11 Product Rule for Exponents

12. 12 Product Rule for Exponents

13. 13 Zero Exponents

14. 14 Zero Exponents

15. 15 Changing the Sign of an Exponent a n and a -n are reciprocals, therefore a -n = (1/a n ) and (1/a -n ) = a n

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18. 18 Scientific Notation Format:a × 10 n × used for multiplication n an integer Example:2 × 10 3 = 2,000

19. 19 Scientific Notation Examples 5,280 = ?.14159 = ?

20. 20 Scientific Notation Examples 5,280 = 5.28 × 10 3.14159 = 1.4159 × 10 -1

21. 21 Converting Standard to Scientific 1. Count the number of places (n) that the decimal point must be moved so that it will follow the first nonzero digit of the number. 2. If the original number was larger than 10, use 10 n. 3. If the original number was smaller than 1, use 10 -n.

22. 22 Converting Scientific to Standard 1. Determine the number of places to move the decimal point by examining the exponent on the 10. 2. Move to the right for a positive exponent and to the left for a negative exponent.

23. 23 Multiplication Example (2,000,000) (0.0000000008) ( 2 × 10 6 ) ( 8 × 10 -10 ) = (2)(8)(10 6 )(10 -10 ) = 16 × 10 -4 = 1.6 × 10 -3 = 0.0016 Scientific Notation is designed for multiplication and division, not addition and subtraction.

24. 24 Light from the Sun Distance to the sun ~ 93,000,000 miles Speed of light ~ 186,000 miles per second Find how long it takes for the light from the sun to reach the earth.

25. 25 Light from the Sun Distance to the sun ~ 93,000,000 miles Speed of light ~ 186,000 miles per second Find how long it takes for the light from the sun to reach the earth.

26. 26 Light from the Sun Distance to the sun ~ 93,000,000 miles Speed of light ~ 186,000 miles per second Find how long it takes for the light from the sun to reach the earth.

27. 27 Light from the Sun Distance to the sun ~ 93,000,000 miles Speed of light ~ 186,000 miles per second Find how long it takes for the light from the sun to reach the earth.

28. 28 Warm-ups

29. 29 The Power Rules

30. 30 Power of a Power Rule

31. 31 Power of a Power Rule

32. 32 Power of a Power Rule

33. 33 Power of a Product

34. 34 Power of a Product

35. 35 Power of a Product

36. 36 Power of a Quotient

37. 37 Power of a Quotient

38. 38 Power of a Quotient

39. 39 Variable Exponents

40. 40 Variable Exponents

41. 41 Integral Exponents

42. 42 Warm-ups

43. 43 Next Slide Show