1. The Zero Exponent Property. This property states that any number (other than
zero itself) raised to the power of zero equals 1. For example,
 = 1,  if x is not zero.  
[However  is not defined.]

2.  The Negative Exponent Property. This property states that any negative
exponent can be converted to a positive by flipping the fraction. For example,
 =  = . 
 = . 


3. The Property of multiplication when there is a common base. This property
states that when multiplying the same base with different exponents, you can
add the exponents together. For example, 
 =  =  = .
 = .

4. The Property of division when there is a common base with different
exponents. This rule states that when dividing the same number with different
exponents, you subtract the exponents. For example
 =  =  = 4.
 =  = .

5.  The Property of multiplication when there is a common exponent with
different bases. This property states that when two or more different numbers
with the same exponent are being multiplied, the exponent is only used once.
For example, 
 =  =  = .
 = .

6.  The Property of division when there is a common exponent with
different bases. This property states that when two or more different numbers
with the same exponent are being divided, the exponent is only used once.
For example,
 =  =  = 8.
 = 

7.  The Power to a Power rule. This rule states that when a power is raised to
another power, you multiply the inner exponent by the outer exponent. For
example, 
 =  =  = .
 =  = .

Edwin