This problem really tests your knowledge of exponents. First, convert x3​ into an exponent, since all of the Roman numerals contain expressions with exponents. (Plus, exponents are easier to work with because they have those nice MADSPM rules.) So, using the definition of a fractional exponent, x3​=x23​. You want the items in the Roman numerals to equal x23​.
Now, it's time to start working with the Roman numerals. In (I), the test writers are trying to be tricky. (There's a surprise.) There's no exponent rule for adding exponent expressions with like bases. So, x+x21​ does not equal x23​. (If you want to be sure, you could try a number for x : If x=4, then 43​=8, but 4+421​ =4+2=6.) So, cross off any answer that includes (I): (B) and (D) are gone.
Now, since you are down to either (A) or (C), all you really need to do is try either (II) or (III). If either one works, the answer is (C). So, try (II). Use the Power-Multiply Rule: (x21​)3=x(21​)(3)=x23​. Since (II) works, (C) is the correct answer.