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### Nested Negative Exponents

```
Date: 8/2/96 at 1:58:23
From: Alfred T Chu
Subject: Negative Exponents

Dear Dr. Math,

Please simplify each expression and write it in a form containing
only positive exponents.

-2     -1   -1
[(-5)   + 3	   ]

Thanks!  I hope you understand this problem and how I typed it.

Sincerely,

Alfred
```

```
Date: 8/6/96 at 10:56:53
From: Doctor Jerry
Subject: Re: Negative Exponents

Dear Alfred,

I will use the notation a^b for a raised to the power b.  This is
easier for typing and is best for e-mail messages, in which spacing
can be changed without notice.

In this notation, your question is

v = ((-5)^(-2) + 3^(-1))^(-1).

Do the outer exponent first.  I'll use the fact that a^(-1) = 1/a.
This gives v = 1/((-5)^(-2)+3^(-1)).

Next, I'll look at the pieces.  First, (-5)^(-2)=1/(-5)^2 = 1/25.
Secondly, 3^(-1) = 1/3.  So, v= 1/(1/25+1/3) = 75/28.

The main rule I used was a^(-1) = 1/a, to get rid of the negative
exponents.

Good luck.

-Doctor Jerry,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Basic Algebra
High School Exponents
Middle School Algebra
Middle School Exponents

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