1. Properties of Exponents – Part 1 Multiplication
Learn multiplication
properties of
exponents.

2. The factors of a power, such as 74, can be grouped in different ways
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

3. MULTIPLYING POWERS WITH THE SAME BASE
Words
Numbers
Algebra
To multiply powers with the same base, keep the base and add the exponents.
bm • bn = bm + n
35 • 38 = = 313
MULTIPLYING POWERS WITH THE SAME BASE

4. Multiplying Powers with the Same Base
Multiply. Write the product as one power.
1. 66 • 63 6
6 + 3
Add exponents. 6 9
2. n5 • n7 n
5 + 7
Add exponents. n 12

5. Multiplying Powers with the Same Base Continued
Multiply. Write the product as one power.
3. 25 • 2 2
5 + 1
Think: 2 = 2 1 2 6
Add exponents.
• 244 24
4 + 4
Add exponents. 24 8

6. Power of Power Property
Powers of powers with the same base:
(am)n = amn
multiply exponents
(24)6 = 224
2(4•6)

7. Power of a Product Property
Different bases, distribute power to each base and multiply.
Examples:
(a • b)4 = a4 • b4 = a4b4
(-3x)2 = (-3) 2• x 2
= 9 x2

8. (32y3)2 (5a2b4)5 3(2•2) y(3•2) 55 a(2•5) b (4•5) 34y6 55a10b20 81y6
Practice!
(32y3)2
3(2•2) y(3•2)
34y6
81y6
(5a2b4)5
55 a(2•5) b (4•5)
55a10b20

9. Practice!
n3  n4
33 • 32 • 35
(-4xy3)3
8 • 88 n7
310
-64x3y9 89