Raising fractions to a power?

[silentthread]

I'm posting in the Geometry and Trig section because my problem is somewhat related to angles. Hopefully it's okay. I apologize if this is not the correct sub forum.

Here is my problem. I get a different answer than the book.

Shouldn't we be able to distrubute the power over each term in the quotient? (see attached 2 pictures of my work and the book answer)

 

[arthur ohlsten]

your second line is a error
1st lkine [sqrt3/3]^2+[sqrt2/2]^2
2nd line should be sqrt9/9 +sqrt4/4

I dislike your method but that is the error
Arthur