Does anyone understand what this question is asking?
The expression is
Multiply and divide by the same number #3^(2/3)
Now, for the denominator, use
Thanks to Andrea for identifying this as the print in ( D ).
Here is a longer answer to your question. (Using different notation.)
We start with
Looking at the list of choices, we see that each choice has an
Looking at the starting expression and the choices of answers, we see that one difference is that the start has a radical (a root) in the denominator and none of the answer choices have that.
What the question is asking us to do is to write an expression that is equivalent to the start, but has no radical in the denominator.
(It's like writing an equal number, but "expression" because of the variable).
AHA! We are being asked to rationalize a denominator. ("Rationalize" mean "make rational".)
Now, for square roots, we know that
The third root has the property that
So we would like to see
We already have
# = (xroot3(3^2))/(root3(3)root3(3^2))#
# = (xroot3(3^2))/root3(3^3)#
# = (xroot3(3^2))/3#
This is not one of the choices, but
I think the solution would be clearer if we had
# = (xroot3(5^2))/(root3(5)root3(5^2))#
# = (xroot3(5^2))/root3(5^3)#
# = (xroot3(5^2))/5#