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:

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

---------------------------------------------------------------------------

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

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

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