Exponent Problem - 5lb Book

[kiricole03]

Question from 5lb Book, Exponents (Chapter 14), #22 - I tried doing this problem and changed the original problem to this -the 44 raised to the 5/2 I changed to the sq root of 44 raised to the 5th power. As far as I understand, in the fraction 5/2, the 5 is the power and the 2 is the index. I did not change the denominator. I then squared the numerator and denominator to get rid of the sq roots on the top and bottom so I ended up with 44^5/11^3. But when I solve the problem I keep getting the wrong answer. Can I square the numerator and denominator the way that I am doing to get rid of the sq roots? Other than that, I have no idea why I am not getting the right answer. The way the book does it, keeping all of the fractional exponents, is a little confusing. So that is why I approached the problem this way, and I thought that it would have worked. Help please!

[tommywallach]

Hey Kiri,

You cannot square the numerator and denominator of a fraction. Watch:

3/4

Square top and bottom:

9/16

Uh-oh! That's a different fraction.

Remember, the only thing you're allowed to do to a fraction is multiply or divide it by versions of 1. When you square top and bottom, you're actually multiplying the top and bottom by different things (in the case of 3/4, as seen above, you're multiplying the numerator by 3 and the denominator by 4).

-t