Division Property of Exponents
Property —
Division Property of Exponents
English To divide two exponential expressions with the same base:
Compare the exponents.
• If the greater exponent is in the numerator, write the
base in the numerator.
• 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 |
![](./articles_imgs/376/algebr38.gif) (Here, m and n are positive integers.) |
![](./articles_imgs/376/algebr39.gif) |
Example 1
a. Use the Division Property of Exponents to find
![](./articles_imgs/376/algebr40.gif)
b. Use the definition of exponential notation to justify your answer.
Note:
Since 3 < 4, we use the form
![](./articles_imgs/376/algebr41.gif)
Solution
a. The bases are the same,
so subtract the exponents.
|
![](./articles_imgs/376/algebr42.gif) |
b. Rewrite the numerator and
denominator to show the factors.
|
![](./articles_imgs/376/algebr43.gif) |
Cancel the common factors. |
![](./articles_imgs/376/algebr44.gif) |
Example 2
Find: 79 ÷ 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.
![](./articles_imgs/376/algebr45.gif)
Note:
Since 9 > 6, we use the form
![](./articles_imgs/376/algebr46.gif)
Example 3
Find: w8 ÷ w13
Solution
The operation is division and the
bases are the same. Therefore, subtract
the exponents and use w as the base.
![](./articles_imgs/376/algebr47.gif)
Note:
Since 8 < 13, we use the form
|