# Req. Help with Fractional Exponent Problem

• Jan 24th 2008, 03:51 AM
Lovely07
Req. Help with Fractional Exponent Problem
Please tell me what I did wrong.
This is a question from my review packet.
The answer says it should be 2 with exponent 3/2

My attempt gives me this:
http://i30.tinypic.com/34rtzmd.jpg
• Jan 24th 2008, 04:01 AM
mr fantastic
Quote:

Originally Posted by Lovely07
Please tell me what I did wrong.
This is a question from my review packet.
The answer says it should be 2 with exponent 3/2

My attempt gives me this:
http://i30.tinypic.com/34rtzmd.jpg

Your mistakes are in the third line. You can't just take the exponents out of the square root like that!!

Note that:

$\displaystyle 2^{5/2} = 2^2 \times 2^{1/2} = 4 \sqrt{2} \,$ and $\displaystyle \, 2^{3/2} = 2^1 \times 2^{1/2} = 2 \sqrt{2}$.

So your problem becomes $\displaystyle 4 \sqrt{2} - 2 \sqrt{2} = 2 \sqrt{2}$.

Now note that $\displaystyle 2 \sqrt{2} = 2^{3/2}$.

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Alternatively, note that $\displaystyle 2^{5/2} = 2^1 \times 2^{3/2} = 2 \times 2^{3/2}$.

So your problem becomes $\displaystyle 2 \times 2^{3/2} - 2^{3/2} = 2^{3/2}$.
• Jan 24th 2008, 04:30 AM
Lovely07
Thank you very much for you help.
The alternative method was easy to understand.