Laws of Exponents Scientific Notation

1
Laws of Exponents Scientific Notation
2
5 x 5
25
52
81
34
3 x 3 x 3 x 3
343
7 x 7 x 7
73
3
52 x 54
56
(5 x 5)
(5 x 5 x 5 x 5)
Do you see a pattern or shortcut?
4
33 x 35
38
(3x3x3)
(3x3x3x3x3)
Do you see a pattern or shortcut?
5
a3 x a5
a8
(a x a x a)
(a x a x a x a x a)
Do you see a pattern or shortcut?
6
Product of Powers Property

• To multiply powers (exponents) with the same
  base, add their exponents.
• a³ x a² a3 2 a5

7
25
2 x 2 x 2 x 2 x 2
22


23
2 x 2 x 2
1
Do you see a pattern or shortcut?
43
45
4 x 4 x 4 x 4 x 4


42
4 x 4
1
8
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

9
REVIEW

• When multiplying- add the exponents
• When dividing- subtract the exponents.

10
EXAMPLES
b10
b7 b3

• 23 22
• 69
• 64

25
z5
Z8 z3
65
11
Zero Exponents

• For any nonzero number a, a0 1
• Anything to the zero power equals 1 (except
  zero)
• 40
• 1000

1
1
12
Negative Exponents

• For any nonzero number a and any integer n,
• a-n 1/an

5-2 1
52
13
1
3-5
3y-2
3
y2
35
1
5-2
a-7b3
b3
52
a7
14
5-8 -3
5-11
5-8 x 5-3
1
or
511
a-2 10
a8
a-2 x a10
15
b-8 5
b-3
b-8 x b5
1
or
b3
3-4 11
37
3-4 x 311
16
35
1
35 - 8
3-3

or

38
33
a6
a8
a6 (-2)


a-2
m2
m2 (-4)
m6


m-4
17
Scientific Notation

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

18
Standard Product Scientific Notation Form Nota
tion 120,000,000 1.2 x 108
1.2 x 100,000,000
19
Write in scientific notation.
4.62 x 109
46,200,000,000
Where is the decimal now?
Move the decimal to the right of the first
significant digit.
20
Write in scientific notation.
8.9 x 107
89,000,000
Where is the decimal now?
Move the decimal to the right of the first
significant digit.
21
Write in scientific notation.
3.04 x 1011
304,000,000,000
Where is the decimal now?
Move the decimal to the right of the first
significant digit.
22
Standard Product Scientific Notation Form Nota
tion 0.00056 5.6 x 10-4
5.6 x 0.0001
23
Write in scientific notation.
5.2 x 10-7
0.00000052
is less than 1 so exponent is negative
Move the decimal to the right of the first
significant digit.
24
Write in scientific notation.
1.06 x 10-9
0.00000000106
is less than 1 so exponent is negative
Move the decimal to the right of the first
significant digit.
25
Write in standard form.
3 2
0
0
0
0
0
0
3.2 x 107
Count the of spaces to move and fill in with
zeros.
Positive Exponents move the decimal to the right
26
Write in standard form.
6 0 4
0
0
0
6.04 x 105
Count the of spaces to move and fill in with
zeros.
Positive Exponents move the decimal to the right
27
Write in standard form.
1.3 x 10-5
1 3
0
0
0
0
Count the of spaces to move left and fill in
with zeros. Then add a decimal point
Negative Exponents move the decimal to the left.
less than 1.
28
Write in standard form.
2.07 x 10-4
2 0 7
0
0
0
Count the of spaces to move left and fill in
with zeros. Then add a decimal point
Negative Exponents move the decimal to the left.
less than 1.
29
Write these in scientific notation.
4.1 x 103
4100
0.000067
6.7 x 10-5
62,000,000
6.2 x 107
0.000000003
3 x 10-9
30
Write these in standard form.
3,040
3.04 x 103
7.2 x 105
720,000
5 x 10-3
0.005
3.8 x 10-6
0.0000038