SUPPLEMENTARY SHEET 5 - NEGATIVE EXPONENTS

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Prof. Howard Sorkin Contact

SUPPLEMENTARY SHEET 5
NEGATIVE EXPONENTS and SCIENTIFIC NOTATION

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GO TO SCIENTIFIC NOTATION

NEGATIVE EXPONENTS

The basic concept of the NEGATIVE EXPONENT is to take the INVERSE or RECIPROCAL of the base to the POSITIVE power.

Rule 1:

Proof:

By the DIVISION RULE:

Therefore:

Examples:

d) REMEMBER TO USE ORDER OF OPERATIONS:

FIRST the EXPONENT.....THEN the DOUBLE NEGATIVE

e) FIRST write WITHOUT the NEGATIVE EXPONENT...

                       ...THEN do the ADDITION PROBLEM
                       This problem was done by first finding the
                       least common denominator.

We will learn a NEW quick and easy way to add or subtract two fractions that do not have a common factor other than 1 in their denominators:

Using the NEW quick and easy way to add the two fractions we have:

Rule 2:

Proof: (using Rule 1)
	This is really a DIVISION problem

Examples:

c) REMEMBER TO USE ORDER OF OPERATIONS:

FIRST the EXPONENT.....THEN the DOUBLE NEGATIVE

Remember: A negative exponent means the INVERSE or RECIPROCAL of the
BASE to the POSITIVE power. In this example

is the BASE.

What we are doing is taking the INVERSE or RECIPROCAL of the BASE to the
POSITIVE power.

GO TO PROBLEMS ON NEGATIVE EXPONENTS

SCIENTIFIC NOTATION -
MULTIPLICATION and DIVISION

Suppose we want to find the answer to the following multiplication problem, written in
STANDARD FORM.

Since we know multiplication is COMMUTATIVE, we can rewrite this problem as
follows:

Of course, there really is no need to rewrite this problem if we are able to calculate

and

in our heads.

We will now find the answer, in STANDARD FORM, to the following division problem:

Since we want our answer to be in STANDARD FORM, when we DIVIDE we
ALWAYS bring the number UP and work out the answer.

REMEMBER, when we move a number either UP or DOWN, the sign of the
exponent changes (see RULE 1 and RULE 2 above).

Here are the steps involved with finding the answer to the DIVISION
problem above.

1. Simplify the part of the problem.

2. Bring UP (it now becomes ) and find this answer.

3. Write the final answer in STANDARD FORM.

Problems 49 - 56 below deal with MULTIPLICATION and DIVISION using
SCIENTIFIC NOTATION.

Find the answers to the following problems:

10.

11.

12.

13.

14.

15.

16.

17.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

41.

42.

43.

44.

45.

46.

47.

48.

49.
50.
51.
52.

ANSWERS

1.	2.	3.	4.	5.	6.	7.	8.
9. 3	10. -3	11. -3	12. 3	13.	14.	15.	16.
17. 1	18. -1	19. 1	20. 2	21. 1	22. -2	23. 1	24. 3x²y
25. -4xy	26. -4x	27. -4	28. 0	29. -2	30. 0	31. -2	32.
33.	34.	35.	36.	37.	38.	39.	40.
41.	42.	43.	44.	45.	46.	47.	48.
49. 584,000,000 50. .078 51. 1.596 52. .000168				53. 260 54. .000027 55. 850,000 56. .0005

Back to NEGATIVE EXPONENT PROBLEMS
Back to SCIENTIFIC NOTATION PROBLEMS