Remark
Let's start with a discussion about the denominator of the given fraction. There are 4 as. They can be written like this. 3rd root of (a * a * a * a ) which can be written as 3rd root (a * a * a) * 3rd root(a). Just to put this in math terms. I'll see if latex will set it up for me.
[tex] \sqrt[3]{a^4} = \sqrt[3]{a * a * a * a} = \sqrt[3]{a * a * a}*\sqrt[3]{a}=3\sqrt[3]{a} [/tex]
What happens to b is not nearly as exciting. It becomes [tex] \sqrt[\frac{2}{3}]{b} [/tex]
Question
What happens to the rest of the given fraction?
Answer
Focus on the as for a second. The given fraction is
a*b^2
-------
a*cuberoot(a) * b^(2/3)
Choice A
Choice A is wrong because the as cancel out.
That leaves you with
b^2
-------
a^(1/3)*b^(2/3)
Since the as are incorrect, the answer is incorrect.
Choice B
Now you have to focus on the b's
b^4
-------
cuberoot(a)*b^(2/3)
I don't know where b^4 came from, but it is never going to work. So choice B is incorrect.
Choice C
Here the b^4 makes sense because it is under the root sign b^2 / b^2/3 = b^(2 -2/3) = b^4/3. There is still a^(1/3) in the denominator. So it is b^(4/3) / a^(1/3) which is exactly what the answer is.
So you actually get C as your answer <<<<< Answer
Choice D would be right except it is written as
a^-(1/3) in the denominator. Or at least that is how I'm seeing it. So d is wrong.
