competency #2 laws of exponents scientific notation
TRANSCRIPT
COMPETENCY #2
Laws of Exponents
Scientific Notation
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