Multiplying Powers
(same base)
Topic Index | Algebra Index | Regents Exam Prep Center

           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:

 
 

...when in doubt, expand terms to see what is happening.

 

 

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 x2y 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: