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# 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

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

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: w8 Ã· w13

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