Basic Exponent Properties

(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

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.

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.

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.

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,