I couldn’t figured out why the answer is C instead of D

For this type of question where there’s no fixed parameter or given, I like to plonk in a number to prevent myself from getting caught off guard

If X = -3, A = undefined and B = -3

If X = 0, A = B = 0

If X = 3, A = B = 3

Since ETS doesn’t recognise a negative term within a radical and X^3 = -3 x -3 x -3 = -27, wouldn’t the answer is we can’t determine the relationship?

Thank you in advance.

Quantity A can be simplified as:

\sqrt[3]{x^3} = (x^3)^{\frac{1}{3}} = x^{(3 \times \frac{1}{3})} = x^1=x

Haha I missed the obvious and cracked my head for nothing. Thanks for the light (as well as your replies in other threads which I will get to it - thank you for taking time).

Just a quick question - seems like for questions with open parameter, I should just reduce or simplify a given term as much as I could before I plonk in numbers to test its range of possible values. Would you agree?

Similar to my reply to HoldMyBeer (what a name!), do you think for questions with an open parameter, I should just reduce or simplify a given term as much as I could before I plonk in numbers to test its range of possible values. What do you think?

It isn’t necessary, but can usually help, as long as the steps you take in simplifying are themselves legal.