## Negative Exponent Problem

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
maroonblazer
Posts: 51
Joined: Thu Aug 12, 2010 11:16 am
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### Negative Exponent Problem

Hi,
The problem states:
"Write the following expression with only positive exponents and in simplest form. Variables are not equal to zero".
$x^{-1} + x^{-5}$

$\frac{x^4+1}{x^5}$

From the initial expression I get:
$\frac{1}{x} + \frac{1}{x^5}$

It's here that I get stuck. The next step seems like it would be:
$\frac{1}{x}+\frac{1}{x(x^5)}$

From there you'd go:
$\frac{1}{2x(x^4)}$

But that seems to go nowhere.

Help?

Thanks,
mb

stapel_eliz
Posts: 1738
Joined: Mon Dec 08, 2008 4:22 pm
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maroonblazer wrote:$\frac{1}{x} + \frac{1}{x^5}$

It's here that I get stuck. The next step seems like it would be:
$\frac{1}{x}+\frac{1}{x(x^5)}$

This would be like trying to convert "1/2 + 1/32" to a common denominator by multiplying 32 by 2, but "2" and "64" aren't "common". Instead, you'd need to convert the "2" to "32": (1/2)(1/16) + 1/32 = 16/32 + 1/32 = (16 + 1)/32.

Use that same process here.

maroonblazer
Posts: 51
Joined: Thu Aug 12, 2010 11:16 am
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### Re: Negative Exponent Problem

Instead, you'd need to convert the "2" to "32":

I love you!

$\frac{1}{x}*\frac{x^4}{x^4} + \frac{1}{x^5}=\frac{x^4+1}{x^5}$

Thank you,
mb