Associated Topics || Dr. Math Home || Search Dr. Math

### 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

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/
```
Associated Topics:
High School Exponents
Middle School Exponents

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search