Rule:
For all numbers x and
all integers m and n ,

"This simply means
... 
when you are multiplying,
and the bases are the same,
you ADD
the exponents." 

Consider:

Observe this
rule at work in the following examples: 

1. 

The bases are the same (all 2's), so the
exponents are added. 

2. 

The bases are the same, so the exponents are
added. Notice how the numbers in front of the bases (7 and
1) are being multiplied. 

3. 

The bases are the same (all a's), so the
exponents are added. 

4. 

The bases are the same (all x's), so the
exponents are added.
Be careful when adding the negative
exponent. 

5. 

The bases are the same, so the exponents are
added.
The numbers in front of the bases are multiplied. 

6. 

The exponents are added for the bases that are
the SAME. The numbers in front, the coefficients, are
multiplied. Don't forget powers of 1, such as the power
associated with t. 

7. 

The exponents are added for the bases that are
the SAME. The coefficients are multiplied. 

8. 

The 9x is multiplied times EACH
term inside the parentheses, adding the exponents as the
multiplication occurs. 

9. 

The ab is multiplied times EACH
term inside the parentheses, adding the exponents of similar
bases as this process occurs. 

10. 

The x^{2}y is multiplied
times EACH term inside the parentheses, adding the exponents of
similar bases as this process occurs. 

Take one more look at the distributive
property at work with a set of parentheses, along with this new rule:
Use the distributive property to simplify:

