The Purpose of Powers

Date: 07/30/2002 at 11:36:08
From: Laura
Subject: Powers

I don't understand the whole purpose of powers, what they do, and how 
to use them. Help me please, Dr. Math.

Date: 07/30/2002 at 12:19:38
From: Doctor Peterson
Subject: Re: Powers

Hi, Laura.

You can find a lot of help with powers in the Dr. Math archives:

   Middle School Exponents
   http://mathforum.org/library/drmath/sets/mid_exponents.html 

I hope you will look through some of the answers that interest you, 
and then write back with any more specific questions you have. This 
might be a good place to start:

    What is an exponent?
    http://mathforum.org/library/drmath/view/58212.html 

To briefly answer your question about the purpose of powers, let's go 
back a couple of years and pretend you only know about addition, and 
not multiplication. Suppose you've heard that multiplication is really 
hard, and you ask me why it is needed. Can you think of some answers 
I might give?

One answer to that is that multiplication lets you state problems 
that would be very big if you just used addition. I can say '17 times 
3' where you would have to say '3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3'.

Another answer is that multiplication gives me a way to calculate big 
sums more quickly. To multiply 17*3, I just have to know 1*3=3 and 
7*3=21, rather than having to add up 17 3's. So multiplication saves 
a lot of time.

That's exactly what powers (or exponents) do for you. Just as 
multiplication (in its simplest form) is just repeated addition, a 
power is just a repeated multiplication. So exponents allow me to talk 
about big problems like 100*100*100*100*100*100*100 by just saying

       7
    100

Once I know this terminology, I can learn the rules of working with 
exponents, so they let me solve problems more quickly. There's a lot 
more you can do down the road using exponents (such as in algebra, 
where they become very important), but this gives you an idea how 
useful they can be.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/