Laws of Exponents

Scientific Notation

Created By:Angie Gallacher

James workman Middle SchoolPalm Springs Unified School District

http://angiegallacher.googlepages.com/

52 = 5 x 5 = 25

34 = 3 x 3 x 3 x 3 =

81

73 = 7 x 7 x 7 =343

52 x 54

(5 x 5) (5 x 5 x 5 x 5)

= 56

Do you see a pattern or shortcut?

33 x 35

(3x3x3) (3x3x3x3x3)

= 38

Do you see a pattern or shortcut?

a3 x a5

(a x a x a)(a x a x a x a x a)

= a8

Do you see a pattern or shortcut?

Product of Powers Property

•To multiply powers (exponents) with the same base, add their exponents.

a³ x a²= a3 + 2 = a5

25

23=

2 x 2 x 2 x 2 x 2

2 x 2 x 2= 22

1

45

42=

4 x 4 x 4 x 4 x 4

4 x 4=

43

1

Do you see a pattern or shortcut?

Quotient of Powers Property

•To divide powers with the same base, subtract the exponent of the denominator from the exponent of the numerator.

68 = 68-5 =63

65

REVIEW

•When multiplying- add the exponents

•When dividing- subtract the exponents.

EXAMPLES

23 • 22 =

69 =64

z5

b1025

65

b7 • b3 =

Z8 =

z3

Zero Exponents•For any nonzero number a, a0 = 1

•Anything to the zero power equals 1 (except zero)

40 =1000 = 1

1

Negative Exponents

•For any nonzero number a and any integer n,

a-n = 1/an

5-2 = 152

3-5 = 1

35

5-2 = 1

52

3y-2 = 3y2

a-7b3 = b3

a7

5-8 x 5-3 = 5-8 + -3 = 5-11

5111or

a-2 x a10 = a-2 + 10 = a8

b-8 x b5 = b-8 + 5 = b-3

b31or

3-4 x 311 =

3-4 + 11 = 37

35

38=35 - 8 =3-3 or

1

33

a6

a-2 =a6 – (-2) = a8

m2

m-4=m2 – (-4) =m6

Scientific Notation

•is a short hand way of writing numbers using powers of 10

Standard Product Scientific Notation Form Notation

120,000,000 1.2 x 108

1.2 x 100,000,000

Write in scientific notation.

46,200,000,000 =

4.62 x 109

Where is the decimal now?

Move the decimal to the right of the first significant digit.

Write in scientific notation.

89,000,000 = 8.9 x 107

Where is the decimal now?

Move the decimal to the right of the first significant digit.

Write in scientific notation.

304,000,000,000 =

3.04 x 1011

Where is the decimal now?

Move the decimal to the right of the first significant digit.

Standard Product Scientific Notation Form Notation

0.00056 5.6 x 10-4

5.6 x 0.0001

Write in scientific notation.

0.00000052 = 5.2 x 10-7

Move the decimal to the right of the first significant digit.

# is less than 1 so exponent is negative

Write in scientific notation.

0.00000000106 =

1.06 x 10-9

Move the decimal to the right of the first significant digit.

# is less than 1 so exponent is negative

3.2 x 107 =

Positive Exponents move the decimal to the right

3 2 0 0 0 00 0

Write in standard form.

Count the # of spaces to move and fill in with zeros.

6.04 x 105=

Positive Exponents move the decimal to the right

6 0 40 0 0

Write in standard form.

Count the # of spaces to move and fill in with zeros.

1.3 x 10-5 =

Negative Exponents move the decimal to the left. # less than 1.

1 300 00

Write in standard form.

Count the # of spaces to move left and fill in with zeros. Then add a decimal point

2.07 x 10-4 =

Negative Exponents move the decimal to the left. # less than 1.

2 0 700 0

Write in standard form.

Count the # of spaces to move left and fill in with zeros. Then add a decimal point

Write these in scientific notation.

4100 4.1 x 103

0.000067 6.7 x 10-5

62,000,000 6.2 x 107

0.000000003 3 x 10-9

Write these in standard form.

3.04 x 103 3,040

7.2 x 105 720,000

5 x 10-3 0.005

3.8 x 10-6 0.0000038