Basic Exponent Properties

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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.

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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.

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.
A18.0 Exponent Properties
by ttor68 | video info

13 ratings | 4,754 views
curated content from YouTube

Exponent Properties Example Set 1

A few examples on how to simplify expressions involving exponents using the basic exponent properties of Algebra.
A18.1 Exponent Properties
by ttor68 | video info

1 rating | 1,726 views
curated content from YouTube

Two More Examples Using the Basic Exponent Properties

A18.4 Power of a Product Example
by ttor68 | video info

1 rating | 1,326 views
curated content from YouTube

Tell Me About Yourself!!!

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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.

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.

Examples of the Division Property of Exponents

A few examples of how to use the division property of exponents.
A18.3 Exponent Properties Involving Fractions
by ttor68 | video info

9 ratings | 7,788 views
curated content from YouTube

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.
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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,

Exponential Growth Example 2

A18.8 Compound Interest Problem
by ttor68 | video info

5 ratings | 4,859 views
curated content from YouTube

Exponential Decay Example 3

A18.9 Exponential Decay Example
by ttor68 | video info

5 ratings | 5,267 views
curated content from YouTube

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.
Math Help Exponents 1: Definitions
by MathTV | video info

44 ratings | 20,638 views
curated content from YouTube

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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 Counts... more »

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