1. Properties of Exponents – Part 1 Multiplication
Learn 3 multiplication properties of exponents.

2. Exponent Vocabulary an = a • a • a…..a n times
Base number: the number being multiplied. a is the base number.
Power: the number of times the base is multiplied. n is the power.

3. 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

4. Multiplication with the same base: am • an = am+n
PRODUCT of POWERS PROPERTY
Multiplication with the same base:
am • an = am+n
Keep base the same and add exponents
Use when you are multiplying a power with another power that has the SAME BASE!
x5 • x8 = x(5+8) = x13

5. Multiplying Powers with the Same Base
Multiply. Write the product as one power.
1. 66 • 63
2. n5 • n7 6
6 + 3
Add exponents n
5 + 7
Add exponents n 12 6 9
If instructions said ‘Evaluate’ or ‘simplify’: would be to simplify fully
=10,077,696
3. 25 • 2
Think: 2 = 2 1
4. z4 • z4 2
5 + 1 z
4 + 4
Add exponents
Add exponents 2 6 z 8
If instructions said ‘Evaluate’ or ‘simplify’
=64

6. Multiplying Powers with the Same Base
Simplify:
5. 52 x4 y • 5 x2 y3 5
2+1
x4+2
y1+3
Add exponents with like bases
53x6y4
Simplify fully
125x6y4

7. Powers of powers with the same base: (am) n = amn
POWER of POWERS PROPERTY
Powers of powers with the same base:
(am) n = amn
Keep base same and multiply exponents
Use when you are raising an entire power to another power, distribute and multiply the exponents (there are not bases that need to match)
(24)6 = 2(4•6) = 224

8. Powers of a product of different bases
POWER of a PRODUCT PROPERTY
Powers of a product of different bases
(a • b)m = am • bm = ambm
distribute power to each base inside and multiply it with existing exponent
Use when you are raising an entire expression to a power, distribute and multiply the exponents (there are not bases that need to match)
(x4y)6 = x(4•6) y(1•6) = x24y6

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

10. Practice! 3. (32y3)2 4. (5a2b4)5 1. (a • b)4 a4 • b4 a4 b4 2. (-3x)2

11. 3y2(2y)3 (r2st3)2(s4t)3 3y2 23y3 = r4s2t6s12t3 = 3 23y5 = r4s14t9
Some final exponent practice problems…
3y2(2y)3 (r2st3)2(s4t)3
3y2 23y3
= 3 23y5
=24y5
= r4s2t6s12t3
= r4s14t9