Name:_________
Date:_________
The Laws of Exponents
Section 1: Law of Multiplying Like Bases
1. Write the following in expanded form. Then write the answer in exponential form with a
single base and power
Exponential Form
Expanded Form
Equivalent Exponential Form
23 × 22
34 × 33
65 × 65
2. What do you notice about the exponents when you multiply two exponents with same base?
________________________________________________________________________
3. Finish the following equation to express what you noticed..
𝑎𝑚 × 𝑎𝑛 = _____________________
Section 2: Law of Dividing Like Bases
1. Rewrite each multiplication sentence as an equivalent division sentence. Use the example
to help you.
Multiplication Sentence
33 × 32 = 35
34 × 33 = 37
65 × 65 = 37
Division by
Divide each side by 32
Equivalent
Sentence
Division
35
3 = 2
3
3
2. What do you notice about the exponents when you divide two exponents with the same
base?
________________________________________________________________________
________________________________________________________________________
3. Why do you think your answer to 2 happens?
________________________________________________________________________
________________________________________________________________________
4. Finish the following equation to express what you have noticed. Assume 𝑎 ≠ 0
𝒂𝒎
𝒂𝒏
=__________________________
Section 3: Law of Raising a Power to a Power
1. Use the example given to help you write the others with a single base and power
Exponential Form
(32 )2
(53 )3
(22 )4
Expanded Form
32 × 32
Equivalent Exponential
Form
34
2. What do you notice about the exponents when you raise a power to a power?
________________________________________________________________________
________________________________________________________________________
3. Finish the following equation to express what you know
(𝐚𝐦 )𝐧 = _______________________
Section 4: Law of Power of a Product
1. Follow Mr. Serra through 3 examples to find this law:
Example 1
Example 2
Example 3
2. Finish the following equation using the examples as a guide
(𝑎𝑚 × 𝑏𝑛 )𝑝 = _____________________
The Laws of Exponents Notes
The Law of Multiplying Like Bases



What it says:
o The Law Multiplying Like Bases says when you multiply two exponents
with the same base you keep the base and add the exponents
What to do:
o Rearrange the multiplication sentence so all coefficients are together and
all like bases are together
o Multiply all coefficients together
o Multiply all like bases together by keeping each base and adding the
exponents for each base
How to do:
o Simplify: 2𝑥 3 × 3𝑥 2
 Rearrange: 2 × 3 × 𝑥 2 × 𝑥 3
 Multiply:
 2x3=6
 𝑥 2 × 𝑥 3 = 𝑥 2+3 = 𝑥 5
 Answer: 6𝑥 5
The Law of Dividing Like Bases



What it says
o When you divide exponents with like bases, we keep the base and subtract the
exponents
What to do
o Divide all coefficients (numbers) first
o Divide all like bases by keeping the base and subtracting the Exponents
o Write your answer as a multiplication sentence
How to do:
4𝑦 6
o Simplify 3
2𝑦
 Divide all coefficients (numbers):
 4÷2=2
 Divide all like bases:

𝒚𝟔
𝒚𝟑
= 𝑦 6−3 = 𝑦 3
 Answer: 2𝑦 3
The Law of Raising a Power to a Power



What it says:
o When we raise a power to a power, we keep the base and multiply the exponents
What to do:
o Keep the base
o Multiply the exponents
How to do:
o Simplify: (𝑥 3 )4
 Keep the base and multiply the exponents: (𝑥 3 )4 =
𝑥 4𝑥3 = 𝑥 12
 Answer: 𝑥 12
The Law of Power of a Product



What it says:
o The Law of Power of a Product says that if we raise a product to a power, we
multiply the exponents. This is a special case of the Power to a Power Law
What to do:
o Keep base 1 and multiply its exponent by the outside exponent
o Keep base 2 and multiply its exponent by the outside exponent
o Write your answer as a multiplication sentence
How to do:
o Simplify: (2x 2 )3
 Keep the base of 2 and multiply the exponents
 21𝑥3 = 23
 Note: When there is no exponent showing, it is
assumed to be 1 since anything raised to 1 is itself
Name:__________
Date:__________
Warm Up: 1/31/14
Directions: Without using your notes, answer each question
1. What does the Law of Multiplying Like Bases state?
________________________________________________________________________
2. What does the Law of Dividing Like Bases state?
________________________________________________________________________
3. What does the Law of Raising a Power to a Power state?
________________________________________________________________________
4. What does the Law of Power of a Product State?
________________________________________________________________________
Score:______________/4
4: You can start on the activity by yourself. This will enhance your knowledge
3: You can start on the activity by yourself. This will help fill in some gaps you might have
2, 1, or 0: Please meet Mr. Serra in the back of the room with your chair. He is going to help you
through the first activity.
Name:_____________
Date:____________
Ticket Out the Door
Directions: Please DO NOT use your notes or each other. This is to be done silently
1. What do we do to the exponents when we multiply two or more exponents with the same
base?
________________________________________________________________________
2. What do we do to the exponents when we raise a power to a power?
________________________________________________________________________
3. What do we do to the exponents when we divide two or more exponents with the same
base?
________________________________________________________________________
4. What do we do to the exponents when we raise a product to a power?
_______________________________________________________________________
Score:______________/4
4: You are good to go with the Laws of Exponents. You are ready for Monday
3: You are ok, but need to study the laws over the weekend to be ready for Monday
2, 1, or 0: You need to make sure you are taking the classwork seriously. You also need to study
over the weekend to be ready for Monday. Maybe look back at the video from Monday night.
Note: If you did not grow from Warm Up to Ticket Out the Door, you need to come to me during
SOAR to have a conference.