Dividing Powers
(same base)
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           Rule:

For all numbers x (not zero) and all integers m and n ,

 

"This simply means ...
when you are dividing,
and the bases are the

same, you SUBTRACT the exponents."
(top exponent subtract bottom exponent)

Consider: ..when in doubt, expand terms

 
 
   

 

Observe this rule at work in the following examples:

  1. 

       

The bases are the same (both 2's), so the exponents are subtracted.

 

2.

     

The bases are the same, so the exponents are subtracted.  Notice how the numbers in front of the bases (7 and 1) are being divided.

 

3.

      

The bases are the same (both a's), so the exponents are subtracted.
Remember:  top exponent minus bottom exponent.

 

4.

      

The bases are the same, so the exponents are subtracted.
The numbers in front of the bases are divided.
 

5.

      

The exponents are subtracted for the bases that are the SAME.  The numbers in front, the coefficients, are divided.

 

6.

      

Notice what happened to the bases with the same exponents -- they reduced to the number 1.

 

7.

    

Remember:  top exponent minus bottom exponent.
Remember:  negative exponents can be written as a fraction.