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### What is an exponent?

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Date: 8/8/96 at 22:23:4
From: Anonymous
Subject: What are "exponents"?

Can you explain what an exponent is? Thanks a lot!
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```
Date: 8/9/96 at 1:7:30
From: Doctor Paul
Subject: Re: What are "exponents"?

An exponent... where to start? Let's first talk about how we denote
exponents.  You may already know that exponents are written above the
number to be exponentionated.  For example:

3
2

When using ASCII, we often do this instead:  2^3
That way, we can get it all on one line.

Now let's talk about what this means.

If you have y^x (y and x are both whole numbers)
then what that really means is

(y)*(y)*(y)...
and you write out x terms..

so 2^3 means:
(2) * (2) * (2) = 8
3^3 =
3*3*3 = 27

get the idea?
Here's how we say it:
2^3 is 'two to the third power'

There are a couple of properties of exponents that you should know

if you have y^-x you can rewrite it as 1/(y^x)

so if you have 2^(-3) that's the same as 1/(2^3)
and we saw earlier that 2^3 is 8, so 2^-3 = 1/8

Get it?

There are other properties:

x^(a+b) = x^a * x^b

so 2^(3+3) = 2^(6)  that's kind of hard to figure out, but using the
above identity it's a lot easier.

2^(3+3) = 2^3 * 2^3 = 8 * 8 = 64

one final property:

(x^a)^b can be written as:
2
[  3]
[ 2 ]

so that's two to the third to the second.  So first take two to the
third and then take that number and take it to the second power.

Well, (x^a)^b = x^(a*b)
so (2^3)^2 is 2^(3*2) =
2^6 = 64

I hope that clears it up.

Regards,

-Doctor Paul,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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Associated Topics:
Elementary Multiplication
Elementary Square Roots
Middle School Exponents

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