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Common Core Standard  N.RN.2

Properties of Exponents Infographic

property of exponents infograhic
x,z ≠ o power of a quotient property
rational exponent property
rational exponent x^(1/y)= √(y&x)  ,x≠0
power of a product  a^C* b^C=(ab)^c,
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a^0 =1 zero exponent
quotient pf powers x^y/x^z = x^(y-z)  ,x≠0
product of powers x^y*x^z= x^((y+z) ),x≠0
power of a quotient
power of a power ( x^y )^z= x^yz
negative exponent  x^(-y )=  1/x^y      x ≠0
​Negative Exponent Property

Power of a Power Property

Power of a Product Property

Power of a Quotient Property

Product of Powers Property

Quotient of Powers Property

Rational Exponent Property

Zero Exponent Property

Properties of Exponents

Exponents are used in Math as a shortcut to tell you how many times to multiply a number by itself. Exponents are sometimes called "powers" or "indices." 
For example: 
Exponents can also be written as follows: 3^2    4^5     6^4

​                               4^5

The video starts with reviewing the rules of negative exponents with basic problems then moves on to more complex examples of negative exponents

Negative Exponents Video

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negative exponents 5^-3 =1/5^3=1divided by 125 =.008
The exponent can also be negative. Think of negative exponents as how many times one can be divided by this number raised to the power of the exponent.

3    =  1 ÷ ( 3 x 3 ) = 1 ÷ 9 = .111

Another way to look at a negative exponent is as follows

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The base
The Exponent
The base
The exponent
4 x 4 x 4 x 4 x 4 = 1024
5 x 5 x 5 = 125
14 Review the Definition of Exponents:
:36 Sample problem multiplying exponents
1:03 Sample problem multiplying negative exponents
1:39 Sample problem with an exponental expression raised to a power
2:15 Sample problem when you have a quantity squared 
3:52 Sample problem negative exponental expression raised to a power
4:02 How to work with a negative exponent
4:19 Simplfying exponential fractions
5:05 Simplfying exponential fractions with positive and negative exponents

Negative Exponents

Reviewing Laws of Exponents

Working with Negative Exponents
5 x 5 x 5
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Properties of Exponents

I created an infographic of the properties of an exponents.

Click on the picture in order to download the infographic
0:22 Introduction to the rules of writing exponents

0:35 Explanation of the parts of an exponent

1:02 Example problem 1 " Writing an exponent"

1:52 Writing an exponent sample proble 2
Properties of Exponents Infographic