The Meaning of Powers, such as Squares and Cubes

Date: 3/14/96 at 18:30:46
From: David Peace
Subject: 5 to the power of 2

Dear Dr. Math,

What does to the power mean?  Like 5 to the power of 2.
I've always wondered that.

   L. R. Green School

Date: 3/14/96 at 23:39:10
From: Doctor Jodi
Subject: Re: 5 to the power of 2

Hi David!

What a good question you wrote to us!  

Powers are just a shorthand. Have you ever seen multiplication 
looked at as grouping?

3 X 5 = 

000
000
000
000
000

or

*****
*****
*****

or

@@@ + @@@ + @@@ + @@@ + @@@   etc..

In the same sort of way, powers are GROUPINGS of multiplications.

So 5 to the power of 2 (also written 5^2) is the same as 5 x 5 
(5 times itself).

I've got a question for you now... What is 5 to the power of 4 (5^4)?

If you want to know more, or if you have more questions, write us 
back...

-Doctor Jodi,  The Math Forum