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Multiplying, Dividing, etc Exponents
This lens is for teachers, parents and students interested in learning about exponents. It includes written and video tutorials on how to deal with exponents. As well it links to other sites that provide explanantions and examples as well. To find the topic you are intested in scroll down or use the table of contents below. Enjoy, and feel free to ask any questions at the bottom of the page.
If you are a teacher looking for resoureces check out my math teaching website. There are some very good worksheets. If you are looking for more math videos check out my videos on youtube.
If you are a student and looking to get all of your math help in one place this math learning site is for you.
Though I think this lens is valuable and can really help you understand exponents sometimes it isn't enough. One of the most effective ways to learn math is one on one tutoring. Tutor.com offers 25 minutes for FREE and is something you should definitely check out.
If you are a teacher looking for resoureces check out my math teaching website. There are some very good worksheets. If you are looking for more math videos check out my videos on youtube.
If you are a student and looking to get all of your math help in one place this math learning site is for you.
Though I think this lens is valuable and can really help you understand exponents sometimes it isn't enough. One of the most effective ways to learn math is one on one tutoring. Tutor.com offers 25 minutes for FREE and is something you should definitely check out.
Table of Contents
(1) Product of Powers, Power of a Power, and Power of a Product - With video tutorial and examples
(2) Zero and Negative Exponent Properties - With video tutorial and examples
(3) Division of Exponent Properties - With video tutorial and examples
(4) Word Problems - Exponential Growth and Decay - With video examples
(5) Other Youtube Videos
(2) Zero and Negative Exponent Properties - With video tutorial and examples
(3) Division of Exponent Properties - With video tutorial and examples
(4) Word Problems - Exponential Growth and Decay - With video examples
(5) Other Youtube Videos
Check Out My Other Lenses on Math
- Single Variable Inequalities
- A lens on solving basic inequalities.
- System of Equations
- A lens illustraing the substitution, elimination and graphing method for solving systems of linear equations.
- Linear Inequalities
- A lense exploring linear inequalities and systems of linear inequalities.
- Solving Quadratic Equations
- A lens show how to solve quadratic equations.
- Polynomials
- A lens showing how to add, subtract, multiply and factor polynomials.
Exponent Properties Part One
Product of a Power, Power of a Power, and Power of a Product
The following video explains three properties of exponents: Product of Powers, Power of a Power and Power of a Product. The properties will be listed below, but it would help your understanding if you viewed the video.
Product of Powers
If two monomials with the same base are multiplied together then you add the exponents.
x3·x2 = x5
or (using symbols)
am·an = am+n
Power of a Power
If a monomial containing powers is raised to a power then you multiply the exponents.
(x4)2 = x8
or (Using symbols)
(am)n = amn
Power or a Product
If a monomial containing more a constant and a variable or more than one variable is raised to a power, then you multiply each exponent by that power. Remember the exponent of a constant is one.
(2x3)4 = 24x8 = 16x8
or (Using Symbols)
(ab)n = anbn
These three properties are shown in more detail in the following video.
Product of Powers
If two monomials with the same base are multiplied together then you add the exponents.
x3·x2 = x5
or (using symbols)
am·an = am+n
Power of a Power
If a monomial containing powers is raised to a power then you multiply the exponents.
(x4)2 = x8
or (Using symbols)
(am)n = amn
Power or a Product
If a monomial containing more a constant and a variable or more than one variable is raised to a power, then you multiply each exponent by that power. Remember the exponent of a constant is one.
(2x3)4 = 24x8 = 16x8
or (Using Symbols)
(ab)n = anbn
These three properties are shown in more detail in the following video.
Remember!!!
Multiplication means Addition
Division means Subtraction
Power means Multiplication
Exponent Properties Tutorial
This is a short video showing why the basic exponent properties work.
Exponent Properties Example Set 1
A few examples on how to simplify expressions involving exponents using the basic exponent properties of Algebra.
Exponent Properties Example Set 2 - Power of a Power
Some examples of how to simplify expressions involving the power of a power.
Two More Examples Using the Basic Exponent Properties
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Zero and Negative Exponent Properties
The next two properties are the zero and negative exponent properties. I will go ahead and list the properties now. The first video describes them in more detail and helps to explain why they work.
Zero Exponent Property
Any quantity raised to a power of zero is equal to one.
3210 = 1
or
(3xy3)0 = 1
or (using symbols)
m0 = 1
Negative Exponent Property
Any quantity raised to a negative power is equal to the the reciprocal of the same quantity raised to the opposite(positive) power.
3-4 = 1/(34)
or (using symbols)
m-n = 1/(mn)
The first video shows how to do this more clearly and the videos after that give you some good examples of zero and negative exponents.
Zero Exponent Property
Any quantity raised to a power of zero is equal to one.
3210 = 1
or
(3xy3)0 = 1
or (using symbols)
m0 = 1
Negative Exponent Property
Any quantity raised to a negative power is equal to the the reciprocal of the same quantity raised to the opposite(positive) power.
3-4 = 1/(34)
or (using symbols)
m-n = 1/(mn)
The first video shows how to do this more clearly and the videos after that give you some good examples of zero and negative exponents.
What Every High School Student Needs!!!
A graphing calculator is an essential tool for a high school math student taking Algebra, Precalculus and Calculus.
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Division of Exponents
Division of exponents is usually the topic that give students the most trouble. It is also the hardest to write about in a website because creating fractions is very difficult. Here is the most important rule and then I am going to encourage you to watch the video below to get a better tutorial.
Division of Exponents Property
When dividing exponent with the same base you subtract the exponents. If the bigger exponent is in the numerator then you subtract in the numerator. If the bigger exponent is in the denominator then you subtract in the denominator.
Division of Exponents Property
When dividing exponent with the same base you subtract the exponents. If the bigger exponent is in the numerator then you subtract in the numerator. If the bigger exponent is in the denominator then you subtract in the denominator.
Examples of the Division Property of Exponents
A few examples of how to use the division property of exponents.
More Examples of the Division Property of Exponents
Let Books be Your Guide
Teachers and students often forget that most things we teach are already written. Here are some great examples of books that could really help learn Algebra.
Algebra I for Dummies
Amazon Price: $13.59 (as of 11/23/2009) 
Algebra Workbook For Dummies
Amazon Price: $11.04 (as of 11/23/2009)
Practical Algebra: A Self-Teaching Guide, 2nd Edition
Amazon Price: $13.57 (as of 11/23/2009)
Studyworks! Teaching Pro: Mathematics Complete
Amazon Price: (as of 11/23/2009)
High School Learning System 2007 (Win/Mac)
Amazon Price: (as of 11/23/2009)
Which Property is the Most Confusing
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Exponential Growth and Decay - Word Problems
The exponential growth and decay formulas are examples of how the exponent properties are used in word problems. The formulas are:
Growth
y = C(1 + r)t
Decay
y = C(1 - r)t
The variables mean the same thing for both formulas.
y = how much you have in the end.
C = how much you started with.
r = the rate expressed as a decimal. 5% = .05
t = the time, the units should coincide with the rate. If it is 5% per year then t should be in years.
The next three videos are examples of how these formulas are used in word problems,
Growth
y = C(1 + r)t
Decay
y = C(1 - r)t
The variables mean the same thing for both formulas.
y = how much you have in the end.
C = how much you started with.
r = the rate expressed as a decimal. 5% = .05
t = the time, the units should coincide with the rate. If it is 5% per year then t should be in years.
The next three videos are examples of how these formulas are used in word problems,
Exponent Worksheets!!!
- Video Examples
- The following problems are the examples in this lens.
- Exponent Properties 1
- This worksheet has examples of the Product of Powers, Power of a Power, and Power of a Product.
Other Websites Discussing Exponents
- Good Examples
- Some good examples on dealing with exponent properties.
- Good Look at Exponent Properties
- This website explains some of the exponent properties.
Other You Tube Videos About Exponents
Here are some other good videos on youtube involving exponents.
curated content from YouTube
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- britany britany May 21, 2008 @ 10:41 am
- I love math because it help me with my career and by getting butter with it thats why I like math.Also you can larn alotr from it and math is everywhere I just love math cause I know all about.
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- karinmarie karinmarie May 13, 2008 @ 1:57 pm
- Thank You so much! This is really going to help me. Thanks!
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- Rebecca_Newburn Rebecca_Newburn Feb 14, 2008 @ 8:20 pm
- Thanks for another great lens and excellent collection of YouTube videos. I'll share it with my students and colleagues. I also added it to my math lenses. Thanks again!
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- jerica jerica Jan 31, 2008 @ 3:59 am
- your great
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- The_Bard The_Bard Jan 29, 2008 @ 10:21 am
- What a superbly commendable lens, and another fine example of Squidoo's community spirit. Thanks for freely imparting your knowledge for the benefit of others. 5*s. - Paul
by MrT68
My name is Trent Tormoehlen and I am a math teacher at Sycamore School in Indianapolis Indiana. I will also be helping coach the schools Math Co...
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