Algebra two homework help, operations with radical expressions?

Okay, the 4 radical you're referring to is known as the fourth root. That's how you say it. So (2/3)^(1/4) is the same as finding the fourth root of 2/3. I'm going to write fourth root as 4rt. Here we go!

4rt(2/3) is the same as (4rt2)/(4rt3). Now you can't have a radical in the denominator of a fraction, so we are going to multiply (4rt3) by something that will give us a number that has a perfect 4th root. So since we have 3 under there, let's start with that. 3^4 = 81. Since we currently only have a 3, we need to multiply by 27 because 3x27=81. So, we are going to do (4rt3) times (4rt27). It has to be 4rt because you can't multiply terms with different radicals/powers. This will give you (4rt81) which equals 3.

So that's how the denominator becomes a plain old 3. How does the numerator become (4rt54)? Well, the basic rule with fractions is that whatever you do to the top, you have to do to the bottom, and vice versa. Basically, you can only multiply or divide a fraction by 1. So what you're really doing here is.... (the dashes are fraction lines)

(4rt2) x (4rt27)

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

(4rt3) x (4rt27)

(4rt2x27)

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

(4rt3x27)

(4rt54)

----------

(4rt81)

(4rt54)

----------

3

Hope this helped you understand the concept. Good luck to you and God bless! :)