1. Section 11-1: Properties of Exponents Property of Negatives:
Suppose m and n are positive integers and a and b are real numbers. Then the following are true:
Property
Definition
Example
 Property of 1:
 Property of 0:
 Property of Negatives:
Product Property
 Power of a Power
 Power of a Quotient
 Power of a Product
 Quotient Property
𝑏 𝑛 = b
5 1 = 5
𝑏 0 = 1
7 0 = 1
𝑏 −𝑛 = 1 𝑏 𝑛
4 −2 = = 1 16
𝑎 𝑚 𝑎 𝑛 = 𝑎 𝑚+𝑛
= = 3 6
𝑎 𝑚 𝑛 = 𝑎 𝑚𝑛
2 𝑥 2 𝑦 3 = 8 𝑥 6 𝑦 3
𝑎 𝑏 𝑚 = 𝑎 𝑚 𝑏 𝑚
𝑥 3 𝑦 = 𝑥 𝑦 8
𝑎𝑏 𝑚 = 𝑎 𝑚 𝑏 𝑚
3𝑥𝑦 = 9 𝑥 2 𝑦 6
𝑎 𝑚 𝑎 𝑛 = 𝑎 𝑚−𝑛
𝑥 5 𝑥 2 = 𝑥 or 𝑥 3 𝑥 9 = 1 𝑥 6

2. c. a. b. d. 5-4 e. f. Example 1 Evaluate each expression.
4 5 ∙ =
= 4 4
= 256 =
= 8 7
a b. = = c. =
= 3 d
e f. =
= 3 6
= 729
(3a-2)3•3a5
= 27 𝑎 −6 3 𝑎 5
= 81 𝑎 −1
= 81 𝑎

3. Example 3 Simplify each expression.
𝑥 2 𝑦 𝑦 3 5
a b.
(s5t2)3
= 𝑠 15 𝑡 6
= 𝑥 2 𝑦 5 𝑦 15
= 𝑥 2 𝑦 10
Example 3 Simplify each expression.
= 𝑎 2
= 𝑎 2
= 2𝑎 2
a b.
= 𝑥 2 6
= 𝑥 1 3
= 𝑥 1 3
= 3 4𝑥

4. Example 4 Evaluate each expression.=
= 3 3
= 27
a b.
= − 1 3 = =
= 3
Example 5
a. Express using rational exponents.
b. Express using a radical.
= 𝑠 𝑡 10 5
= 𝑠 5 𝑡 2
= 2𝑠 5 𝑡 2
20 4 𝑥 3 𝑦

5. 𝑟 5 𝑠 15 𝑡 4
Example 6 Simplify:
= 𝑟 2 𝑠 7 𝑡 𝑟𝑠
= 𝑟 2 𝑠 7 𝑡 2 𝑟𝑠
Example Solve: =
343= 𝑥 3 2
= 𝑥
= x
7 2 = x
49 = x