Question

What’s the answer? Plz explain.

Answer 1

Thus option C is the answer

Answer 2

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.

`\sqrt[3]{a^4} = \sqrt[3]{a * a * a * a} = \sqrt[3]{a * a * a}*\sqrt[3]{a}=3\sqrt[3]{a}`

What happens to b is not nearly as exciting. It becomes
`\sqrt[(2)/(3)]{b}`

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.