1. Multiplication and Division of Powers
We will often want to be able to multiply and divide powers that have the same base.
An example of Multiplication of Powers
An example of Division of Powers

2. Consider the following multiplication of powers:
This suggests the property for the Multiplication of Powers.
Let b represent a real number and m and n represent positive integers. Then …

3. Consider the following division of powers:
This suggests the property for the Division of Powers.
Let b represent a real number and m and n represent positive integers. Then …

4. Example 1
Both bases are the same, so apply the property of multiplication of powers:

5. Example 2
Since the bases are not the same, we cannot use the property of multiplication of powers.

6. Example 3
Both bases are the same, so apply the property of multiplication of powers:

7. Example 4
Both bases are the same, so apply the property of division of powers:

8. Example 5
Both bases are the same, so apply the property of division of powers:

9. Example 6
This problem uses both of the properties. Note that all of the bases are the same.
First apply the multiplication property in the numerator:

10. Now apply the division property:

11. Example 7
Note that all of the bases are the same.
First apply the multiplication property in the denominator:

12. Now apply the division property:

13. END OF PRESENTATION