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Product of Powers Property


Introduction

An exponent is a mathematical operation that can be used for repeated multiplication.  The number of the exponent tells you how many times to repeat the multiplication.

62 = 6 × 6                         53 = 5 × 5 × 5                                24 = 2 × 2 × 2 × 2


Lessons

Each exponential expression has two parts: a base and an exponent (exponents can also be called powers).  Exponents are a quick and efficient way to show a repeated multiplication.

Prod_of_Powers_vis_1 

The two examples above demonstrate how to evaluate an exponent.  What do you do if you have several different exponential terms multiplied together?  Consider the problem 53 × 54.

Prod_of_Powers_vis_2 

 

In the problem above, the two expressions being multiplied both have a base of five.  The work above shows that the exponents can simply be added.  Here is another way to look at the work in similar problems.

 

Prod_of_Powers_vis_3 

 

The rules are the same whether the bases are numbers or variables.  This property that allows you to multiply two exponential expressions with the same base is called the product of powers property.

 

Prod_of_Powers_vis_4 

 

This property works as long as the bases are the same in each of the exponential terms being multiplied. 

 

Examples:

 

Prod_of_Powers_vis_5Prod_of_Powers_vis_68aProd_of_Powers_vis_7Prod_of_Powers_vis_68aProd_of_Powers_vis_9Prod_of_Powers_vis_10a 

 

 

However, if the bases are different, then the product of powers property cannot be applied.

 

 

Prod_of_Powers_vis_11 

 

 

More Complex Problems

When dealing with problems that involve several different variables, multiply each variable separately and then combine the results to get your answer.

 

Prod_of_Powers_vis_12Prod_of_Powers_vis_13 

 

If you are even in doubt about how to do a problem that deals with exponents, consider expanding the exponents and then putting like terms together.  For example, x2∙x3 = x∙x ∙ x∙x∙x = x5.  Showing the work in this way may take a little extra time, but your extra time is worth it because you will be more confident in your answer and in your ability to do these types of problems.

 

Review

Use the power of products property to multiply:

 

1)  a2a3a4 =

2)  x4y2∙z7 =

3)  m2n7 m3n4 =

4)  22s4t6 ∙ 5s6t11 =

5)  9de5f8 ∙ 2d3e3f5 =

 

Scroll Down for Answers…

 

 

 

 

 

  

 

Use the power of products property to multiply:

1)  a2a3a4 = a9

2)  x4y2∙z7 = x4y2∙z7

3)  m2n7 m3n4 = m5n11

4)  22s4t6 ∙ 5s6t11 = 20s10t17

5)  9de5f8 ∙ 2d3e3f5 = 18d4e8f13

 


 

 

 

Related Links:

Didn't find what you were looking for in this lesson?  More information on exponents can be found at the following places:


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Related Algebra Lessons

 

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