The Purplemath Forums

by **maroonblazer** on Sun Dec 04, 2011 12:33 am

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

The answer is:
$\frac{x^4+1}{x^5}$

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

**Sponsor**

by **stapel_eliz** on Sun Dec 04, 2011 1:51 am

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. :wink:

by **maroonblazer** on Sun Dec 04, 2011 6:22 am

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

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