Division Property of Exponents
Property â€”
Division Property of Exponents
English To divide two exponential expressions with the same base:
Compare the exponents.
â€¢ If the greater exponent is in the numerator, write the
base in the numerator.
â€¢ If the greater base is in the denominator, write the base
in the denominator.
Then subtract the smaller exponent from the greater.
Use the result as the new exponent.
Algebra 
Example 
(Here, m and n are positive integers.) 

Example 1
a. Use the Division Property of Exponents to find
b. Use the definition of exponential notation to justify your answer.
Note:
Since 3 < 4, we use the form
Solution
a. The bases are the same,
so subtract the exponents.


b. Rewrite the numerator and
denominator to show the factors.


Cancel the common factors. 

Example 2
Find: 7^{9} Ã· 76. Leave your answer in exponential notation.
Solution
The operation is division and the
bases are the same. Therefore, subtract the exponents and use 7 as the base.
Note:
Since 9 > 6, we use the form
Example 3
Find: w^{8} Ã· w^{13}
Solution
The operation is division and the
bases are the same. Therefore, subtract
the exponents and use w as the base.
Note:
Since 8 < 13, we use the form
