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### Negative Fraction Exponents

```
Date: 01/27/99 at 09:39:26
From: Khalida
Subject: Pre-calculus Exponents

2n^(1/3) - 4n^(-2/3)
-------------------
2n^(-2/3)

I am having trouble with these kinds of problems. If you could help me
simplify these exponents and also radical exponents, I would be very
thankful.

Khalida
```

```
Date: 01/27/99 at 12:55:13
From: Doctor Rick
Subject: Re: Pre-calculus Exponents

Hi, Khalida.

I would start by breaking this into a difference of two fractions (by
applying the distributive principle).

1/3      -2/3
2n       4n
------ - -------
-2/3     -2/3
2n       2n

Now, you can see right off that in each fraction, the numerator and
denominator are both divisible by 2. So divide numerators and
denominators by 2:

1/3      -2/3
n       2n
----- - -------
-2/3     -2/3
n        n

What's left is the part you are most concerned about, I'm sure. Here
are two rules you can use:

x^n / x^m = x^(n-m)

1 / x^n = x^(-n)

Use the second rule to convert each fraction (division) into a product:

1/3    2/3    -2/3    2/3
n    * n    - 2n    * n

Then use the first rule to combine the powers of n:

(1/3 + 2/3)     (-2/3 + 2/3)
n            - 2n

1     0
n  - 2n

which we can write as

n - 2

Wow, that's a lot simpler!

You can simplify expressions with radicals in the same way, if you
first rewrite each radical as a fractional power, for instance,
sqrt(x) = x^(1/2). If you need more help with radicals, send an
example, and we'll work through it.

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

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