Section: 1.4
Date:
Use the rules of exponents to simply expressions.
Objective
Zero Exponents
For any real number 𝑎: 𝑎0 = 1.
Negative Exponents For any real numbers 𝑎 and 𝑛: 𝑎−𝑛 = 1 or 1 = 𝑎𝑛 .
𝑎𝑛
𝑎−𝑛
Rules for Exponents
Examples
What is the simplified form of each expression?
1
a. 5𝑎3 𝑏 −2
b. 𝑥 −5
Practice
What is the simplified form of each expression?
a.
𝑛−5
𝑚2
b.
2
𝑥0
Multiplying Powers
with the Same Base
Examples
For any real numbers 𝑎, 𝑚, and 𝑛: 𝑎𝑚 𝑎𝑛 = 𝑎𝑚+𝑛 .
Practice
What is the simplified form of each expression?
a. 5𝑥 4 ∙ 𝑥 9 ∙ 3𝑥 −2
b. −4𝑐 3 ∙ 7𝑑 2 ∙ 2𝑐 −3
Raising a Power to
a Power
Examples
For any real numbers 𝑎, 𝑚, and 𝑛: (𝑎𝑚 )𝑛 = 𝑎𝑚𝑛
What is the simplified form of each expression?
a. 4𝑧 5 ∙ 9𝑧 −12
b. 2𝑎 ∙ 9𝑏 4 ∙ 3𝑎2
What is the simplified form of each expression?
a. (𝑛4 )7
Practice
What is the simplified form of each expression?
a. (𝑝4 )5
Raising a Product
to a Power
2 1
b. (𝑥 3 )2
1 1
b. (𝑝2 )4
For any real numbers 𝑎, 𝑏, 𝑚, and 𝑛: (𝑏𝑎𝑚 )𝑛 = 𝑏 𝑛 𝑎𝑚𝑛 .
Examples
What is the simplified form of each expression?
1
2
b. (𝑛2 )10 (4𝑚𝑛−3 )3
a. (7𝑚9 )3
Practice
What is the simplified form of each expression?
a. (2𝑧)−4
b. (𝑥 −2 )2 (3𝑥𝑦 5 )4
Dividing Powers
with the Same Base
For any real numbers 𝑎, 𝑚, and 𝑛:
Examples
What is the simplified form of each expression?
a.
Practice
𝑚2 𝑛 4
𝑚5 𝑛 3
𝑎𝑚
𝑎𝑛
= 𝑎𝑚−𝑛 .
5
b.
𝑥2
𝑥2
What is the simplified form of each expression?
a.
𝑥 4 𝑦 −1 𝑧 8
𝑥 4 𝑦 −5 𝑧
3
b.
𝑦4
1
𝑦2
𝑎𝑚 𝑝
Raising a Quotient
to a Power
For any real numbers 𝑎, 𝑏, 𝑚, 𝑛, and 𝑝: ( 𝑏𝑛 ) =
Example and
Practice
What is the simplified form of each expression?
2
𝑧3
3
a. ( 5 )
3
𝑎4
4
b. (𝑎5 )
𝑎𝑚𝑝
𝑏 𝑛𝑝
.