Download Properties of Exponents - Jamestown Public Schools

2-7 Properties of Exponents
Warm Up
Evaluate.
1. 33
27
2. 4 • 4 • 4 • 4
256
3. b2 for b = 4
16
4. n2r for n = 3 and r = 2
18
Course 3
2-7 Properties of Exponents
Learn to apply the properties of exponents
and to evaluate the zero exponent.
Course 3
2-7 Properties of Exponents
The factors of a power, such as 74, can be
grouped in different ways. Notice the
relationship of the exponents in each product.
7 • 7 • 7 • 7 = 74
(7 • 7 • 7) • 7 = 73 • 71 = 74
(7 • 7) • (7 • 7) = 72 • 72 = 74
Course 3
2-7 Properties of Exponents
MULTIPLYING POWERS WITH THE SAME BASE
Words
Numbers
To multiply
powers with
35 • 38 =
the same base, 5 + 8
3
= 313
keep the base
and add the
exponents.
Course 3
Algebra
bm • bn =
bm + n
2-7 Properties of Exponents
Additional Example 1A & 1B: Multiplying Powers with
the Same Base
Multiply. Write the product as one power.
A. 66 • 63
66 + 3
69
Add exponents.
B. n5 • n7
n5 + 7
n 12
Add exponents.
Course 3
2-7 Properties of Exponents
Additional Example 1: Multiplying Powers with the
Same Base Continued
Multiply. Write the product as one power.
C. 25 • 2
25 + 1
26
Think: 2 = 2 1
Add exponents.
D. 244 • 244
24 4 + 4
24 8
Course 3
Add exponents.
2-7 Properties of Exponents
Try This: Example 1A & 1B
Multiply. Write the product as one power.
A. 42 • 44
42 + 4
46
Add exponents.
B. x2 • x3
x2 + 3
x5
Add exponents.
Course 3
2-7 Properties of Exponents
Notice what occurs when you divide powers
with the same base.
55555
55555
55
2
=
5
•
5
=
=
=
5
555
555
53
DIVIDING POWERS WITH THE SAME BASE
Words
To divide powers
with the same
base, keep the
base and subtract
the exponents.
Course 3
Numbers
6 9 = 69 – 4 = 6 5
64
Algebra
b m = bm – n
bn
Remember
Multiply: add exponents
Divide: subtract exponents
2-7 Properties of Exponents
Additional Example 2: Dividing Powers with the Same
Base
Divide. Write the product as one power.
A.
5
7
3
7
75 – 3
7
Subtract exponents.
2
10
B. x9
x
x10 – 9
x
Course 3
Subtract exponents.
Think: x1 = x
2-7 Properties of Exponents
Try This: Example 2
Divide. Write the product as one power.
A.
99
92
99 – 2
97
B.
e 10
e5
e10 – 5
5
e
Course 3
Subtract exponents.
Subtract exponents.
2-7 Properties of Exponents
THE ZERO POWER
Words
Numbers
The zero power of
any number
except 0 equals 1.
1000 = 1
(–7)0 = 1
Algebra
a0= 1, if a  0
Anything to the zero power equals 1
Course 3
2-7 Properties of Exponents
Negative Exponents
When you have a negative exponent,
take the reciprocal and make the
exponent positive.
1
x  n
x
n
1
4  3
4 
3
Course 3

1
7  2
7
2

1
a  5
a
5
2-7 Properties of Exponents
Lesson Quiz: Part 1
Write the product or quotient as one power
1. n3  n4
n7
2. 8 • 88
89
109
3.
105
104
t9
4.
t7
5. 5
Course 3
2
t
1
25
2
2-7 Properties of Exponents
Lesson Quiz: Part 2
6. A school would like to purchase new
globes. They can get six dozen for
$705.80 from Company A. From
Company B, they can buy a half gross
for $725.10. Which company should
they buy from? (1 gross = 122 items)
Company A
Course 3