ofofExponents
4-3
4-3 Properties
Properties
Exponents
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
33
4-3 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
4-3 Properties of Exponents
Problem of the Day
Calculate 6 to the fourth power minus 56.
1240
Course 3
4-3 Properties of Exponents
Learn to apply the properties of exponents.
Course 3
4-3 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
4-3 Properties of Exponents
Course 3
4-3 Properties of Exponents
Additional Example 1: 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
4-3 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.
4-3 Properties of Exponents
Check It Out: Example 1
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
4-3 Properties of Exponents
Check It Out: Example 1
Multiply. Write the product as one power.
C. x5 • y2
x5 • y2
Cannot combine; the bases are
not the same.
D. 412 • 417
41 2 + 7
41 9
Course 3
Add exponents.
4-3 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
Course 3
4-3 Properties of Exponents
Additional Example 2: Dividing Powers with the Same
Base
Divide. Write the quotient 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
4-3 Properties of Exponents
Check It Out: 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.
4-3 Properties of Exponents
RAISING A POWER TO A POWER
Reading Math
4 5
(9 ) is read as “nine to the
fourth, to the fifth.”
Course 3
4-3 Properties of Exponents
Additional Example 3: Raising a Power to a Power
Simplify.
A. (54)2
(54)2
= 54 • 2 Multiply exponents.
= 58
B. (67)9
(67)9
= 67 • 9 Multiply exponents.
= 663
Course 3
4-3 Properties of Exponents
Additional Example 3: Raising a Power to a Power
Simplify.
C.
2
3
12 –3
Multiply exponents.
=
2
3
12 • –3
2 –36
=
3
Course 3
D. (172)
(172)
–20
–20
Multiply exponents.
= 172 • –20
= 17–40
4-3 Properties of Exponents
Check It Out: Example 3
Simplify.
A. (33)4
(33)4
= 33 • 4 Multiply exponents.
= 312
B. (48)2
(48)2
= 48 • 2 Multiply exponents.
= 416
Course 3
4-3 Properties of Exponents
Check It Out: Example 3
Simplify.
C.
1
4
11 –2
Multiply exponents.
=
1
4
11• –2
1 –22
=
4
Course 3
D. (134)
(134)
–10
–10
Multiply exponents.
= 134 • –10
= 13–40
4-3 Properties of Exponents
Lesson Quiz
Write the product or quotient as one power.
1. n3  n4
109
3.
105
Course 3
n7
104
2. 8 • 88 89
t9
4.
t7
t2
5. 32 • 33 • 35 310
6. (m2)19 m38
7. (9-8)9 9–72
8. (104)0
1