# Thread: Req. Help with Fractional Exponent Problem

1. ## 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:

2. 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:
Your mistakes are in the third line. You can't just take the exponents out of the square root like that!!

Note that:

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

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

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

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

So your problem becomes $2 \times 2^{3/2} - 2^{3/2} = 2^{3/2}$.

3. Thank you very much for you help.
The alternative method was easy to understand.