AFDA – Unit 6: Exponents and Radicals
Day 1 Notes: Laws of Exponents
Name: _________________
Block: _____ Date:_______
Today we will…
 Discuss the laws of exponents
 ________________ show repeated multiplication.
 Exponents represent how many times a number (____________________) is
multiplied by itself.
Exponential Form: 95
Word Form: Nine to the fifth power
Expanded (Factor) Form: 9 ∙ 9 ∙ 9 ∙ 9 ∙ 9
Standard Form: 59,049
Law of Exponents
Law
Math Lingo
Example
Zero Power
𝑎0 = 1
910 = 1
Product of Powers
𝑎𝑚 ∙ 𝑎𝑛 = 𝑎𝑚+𝑛
𝑥3 ∙ 𝑥4 = 𝑥7
Quotient of Powers
𝑎𝑚
= 𝑎𝑚−𝑛
𝑎𝑛
𝑦5
= 𝑦3
𝑦2
Power to a Power
(𝑎𝑚 )𝑛 = 𝑎𝑚∙𝑛
(𝑧 4 )3 = 𝑧 12
Negative Power (“Elevator
Ride”)
𝑎−𝑚 =
1
𝑎𝑚
or
1
𝑎−𝑚
= 𝑎𝑚
𝑐 −2 =
1
𝑐2
Power of a Product
(𝑎𝑏)𝑚 = 𝑎𝑚 𝑏 𝑚
(3𝑑)3 = 33 𝑑 3 = 27𝑑 3
Power of a Quotient
𝑎 𝑚 𝑎𝑚
( ) = 𝑚
𝑏
𝑏
𝑒 3 𝑒3 𝑒3
( ) = 3=
4
4
64
Law
Zero Power
What?
Any number to the 0 power
always equals 1
3 0
1. ( )
4
2. 𝑦 0
3. (𝑥 4 )0
4.
Math Lingo
𝑎0 = 1
Law
What?
Math Lingo
Product of Powers
“Add” the exponents
𝑥3 ∙ 𝑥4 = 𝑥7
1. 𝑥 2 ∙ 𝑥 3
2. 24 ∙ 25
3. 10𝑥 2 ∙ 3𝑥 4
4.
Law
Quotient of Powers
1.
3.
𝑟9
𝑟4
𝑠 7 𝑡 9 𝑢3
𝑠4𝑡 7𝑢
What?
“Subtract”/cancel out
exponents
2.
4.
410
46
Math Lingo
𝑎𝑚
= 𝑎𝑚−𝑛
𝑎𝑛
Law
What?
Math Lingo
Power to a Power
Multiply exponents
(𝑎𝑚 )𝑛 = 𝑎𝑚∙𝑛
1. (𝑥 2 )4
2. (33 )6
3. (𝑥 2 )3+𝑦
4.
Law
Negative Power (“Elevator
Ride”)
1. 𝑔−4
3. 4−3 𝑥 2
5.
What?
Math Lingo
𝑎−𝑚 =
Switch location
2.
4.
6.
1
ℎ−7
1
2𝑥 −5
1
𝑎𝑚
or
1
𝑎−𝑚
= 𝑎𝑚
Law
What?
Math Lingo
Power of a Product
Distribute to the exponents
(𝑎𝑏)𝑚 = 𝑎𝑚 𝑏 𝑚
1. (𝑥 2 𝑦 4 )3
2. (2𝑥 2 )4
3. (−4𝑥 3 )2
4.
Law
What?
Power of a Quotient
Distribute to the exponents
1.
3.
𝑟 𝑡
(𝑠 )
2 2
(3)
2.
4.
𝑥2
4
(𝑦 3 )
Math Lingo
𝑎 𝑚 𝑎𝑚
( ) = 𝑚
𝑏
𝑏
My brain hurts.
1.
3.
8𝑥𝑦 2
81𝑎3 𝑏 3 𝑐 4
2.
(3𝑎𝑏 −2 𝑐 2 )2
12𝑥 −3 𝑦 5
2𝑥 −2 𝑦 3
8𝑥𝑦 2
−3𝑥𝑦 5
∙ 4𝑥 −5 𝑦 −2
4.
4𝑥 −1 𝑦 2 −5𝑥 4 𝑦 6
2𝑥3𝑦 2
∙ 2𝑥 3 𝑦 −1