2. Let’s start by reviewing what you know …

4. Exponents … PowersWhen you take a number to a positive power, you multiply it by itself repeatedly.

5. 3 5 = 33333 = 2432 7 = 2222222 = 128(-4) 3 = (-4)(-4)(-4) = -64(-3) 2 = (-3)(-3) = 90 8 = 00000000 = 0

6. Write 77777 with exponents

7. Write 77777 with exponents 7 5

8. The number that is taken to a power is called the base.

9. Rules for working with exponents: Product Rulex n x m = x n+mWhen you multiply things with exponents, add the exponents.

10. 3 2 3 4 = 3 6(5 9 )(5 3 ) = 5 12n 8 n 8 = n 16

11. What is (w 3 x 2 y 5 z 3 )(x 3 yz 6 ) ?

12. What is (w 3 x 2 y 5 z 3 )(x 3 yz 6 ) ? w 3 x 5 y 6 z 9

13. What is (2 x )(2 y ) ?

14. What is (2 x )(2 y ) ? 2 x+y

15. Quotient Rule   When you divide or make a fraction out of things with exponents, subtract the exponents.

16. 5 9  5 3 = 5 6or just 7

17. Power Rule(x n ) p = x npWhen you raise a power to a power, multiply the exponents.

18. (5 3 ) 2 = 5 6(8 9 ) 5 = 8 45(2 2 ) 4 = 2 8

19. What is (w 2 xy 4 z 3 ) 5 ?

20. What is (w 2 xy 4 z 3 ) 5 ? w 10 x 5 y 20 z 15

21. Zero Exponent Rulex 0 = 1If you raise anything (except 0) to the zero power, the answer is always 1.3 0 = 15 0 = 110 0 = 1

23. You know that any fraction with the same numerator and denominator equals 1.

24. But … when there are exponents in the fraction, you can subtract exponents. If the numerator and denominator are the same, you get a zero exponent.

25. Since these equal the same fractions, the zero exponents equal 1.

27. Negative Exponent RuleWhen you take something to a negative power, it makes a fraction (reciprocal).

28. 5 -1 = 1 / 53 -2 = 1 / 92 -3 = 1 / 8

29. Other Useful Rules …  (xy) p = x p y p 

30. For example … 50 3 = 5 3 x 10 3 = 125 x 1000 = 125,000

32. Scientific Notationa shorthand way to write very large or very small numbersIn scientific notation, numbers always have the form ____ X 10--.

36. To change a number into scientific notation …Move the decimal so there is just one place before it.Count the places after the decimal

37. Example: Change 53,700,000,000 to scientific notation

38. Example: Change 53,700,000,000 to scientific notation 5.37 x 10 10

39. Example: Change 435,300,000 to scientific notation

40. Example: Change 435,300,000 to scientific notation 4.353 x 10 8

41. If the number is already a decimal, you still move the decimal so there is just one place before it.Count how many places you moved the decimal; the exponent is negative that number. (This is always one more than the number of 0’s after the original decimal.)

42. Example: Change.000412 to scientific notation.

43. Example: Change.000412 to scientific notation. 4.12 x 10 -4

44. Example: Change.00000000000024 to scientific notation

45. Example: Change.00000000000024 to scientific notation 2.4 x 10 -13

47. To change back to decimal notation …Copy the significant digitsIf the exponent is positive, there are that many places after the first digit; add zeros to make the number of places.If the exponent is negative, put in one fewer zeros than the exponent at the beginning.

48. Example: Change 3.7 x 10 5 to decimal notation.

49. Example: Change 3.7 x 10 5 to decimal notation. 370,000

50. Example: Change 5.417 x 10 12 to decimal notation.

51. Example: Change 5.417 x 10 12 to decimal notation. 5,417,000,000,000

52. Example: Change 3.4 x 10 -5 to decimal notation.

53. Example: Change 3.4 x 10 -5 to decimal notation..000034

54. Example: Change 2.456 x 10 -7 to decimal notation

55. Example: Change 2.456 x 10 -7 to decimal notation.0000002456