multiplication

1. Multiplying
Exponential
Expressions

2. Write 34 in expanded notation.
3 . 3 . 3 . 3
Write 35 in expanded notation.
3 . 3 . 3 . 3 . 3
Observe this expression: 34 . 35

3. (3 . 3 . 3 . 3) . (3 . 3 . 3 . 3 . 3)
Observe this expression: 34 . 35
Let’s take out the parenthesis:
3 . 3 . 3 . 3 . 3 . 3 . 3 . 3 . 3
34 . 35 = 39

4. (2 . 2 . 2) . (5 . 5)
How do we combine this expression into one?
23 . 52
Let’s take out the parenthesis:
2 . 2. 2 . 5 . 5
Since we have different bases, let’s leave it as 2352

5. The Rule:
•So when we had 34. 35, we have four 3’s multiplied
together and multiplied further by five 3’s multiplied
together. Altogether we have nine 3’s or 39
•When multiplying two numbers having different
exponents but the same bases, we simply copy the base
and add the exponents.
33 . 35
xm . xn =
m+n