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. 

