1. 6.2 Multiplying Powers with the Same Base
I can multiply powers with the same base.
6.2 Multiplying Powers with the Same Base

2. Product of Powers
You can write the product of powers with the same base using only one exponent.
Ex: 3 4 ∙ 3 2
(3∙3∙3∙3)(3∙3)
3 6
What do you notice?

3. How to Multiply
Notice in the previous example ( 3 4 ∙ 3 2 = 3 6 ) that the sum of the exponents in the expression equals the exponent of the answer.
In general, 𝑎 𝑚 ∙ 𝑎 𝑛 = 𝑎 𝑚+𝑛
Meaning, when multiplying and bases are the same, add the exponents.

4. Practice
12 4 ∙ 12 3
12 7
(−5) −2 (−5) 7
(−5) 5

5. Algebraic Expressions
4 𝑧 5 ∙9 𝑧 −12
The base is z
Since multiplication is commutative:
4∙9∙ 𝑧 5 ∙ 𝑧 −12
Associative
(4∙9)( 𝑧 5 ∙ 𝑧 −12 )
36 𝑧 −7
36 𝑧 7

6. You Try
2𝑎∙9 𝑏 4 ∙3 𝑎 2
2∙9∙3∙𝑎∙ 𝑎 2 ∙ 𝑏 4
54 𝑎 3 𝑏 4