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### Subtracting Exponents when Dividing Like Bases

```Date: 01/21/2005 at 16:36:27
From: snarles
Subject: my question is about simplifying variables

I need to simplify x to the seventh power over x to the third power.
I think I should divide 7 by 3 and put that as the power, but I end up
with x to the 2.3 repeating power, and the book says it's x to the
fourth power.

```

```
Date: 01/21/2005 at 18:10:11
From: Doctor Achilles
Subject: Re: my question is about simplifying variables

Hi Snarles,

Thanks for writing to Dr. Math.

x to the seventh
------------------
x to the third

Now, remember that x to the seventh is shorthand for x*x*x*x*x*x*x

(The * is a multiplication symbol.)

x*x*x*x*x*x*x
---------------
x*x*x

Ok, so the first step in reducing a fraction is to find a common
factor in the top and bottom.  One common factor is x:

x*(x*x*x*x*x*x)
-----------------
x*(x*x)

Now we cancel out the common factor and we are left with:

x*x*x*x*x*x
-------------
x*x

Now find another common factor:

x*(x*x*x*x*x)
---------------
x*(x)

And we get:

x*x*x*x*x
-----------
x

And again, we find a common factor:

x*(x*x*x*x)
-------------
x*(1)

And we get:

x*x*x*x
---------
1

Or just:

x*x*x*x

Or just:

x to the fourth power

You may have heard the rule "When you divide like bases with
exponents, subtract the powers" or something like that.  What that
means is when you have something like:

x to the seventh
------------------
x to the third

x to the (7-3)

Or:

x to the fourth

Hope this helps.  If you have other questions or you'd like to talk

- Doctor Achilles, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Exponents

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