Tricky question. We do not know anything about K and x could be anything also. The variation of the values could be also infinite

D is the answer.

However, even picking numbers, the solution is straight and D as well

Suppose K=0 and X=1

A is 1/1 and B is 1. So C is the answer

BUT

K=1
x=1

A is \(\frac{2^2}{2^4} = \frac{1}{2^2}=\frac{1}{4}=0.25\)

B is \(2^{\frac{1}{2}}=\sqrt{2}=1.4\)

B is the answer

Two conflict answers

D is the final pick

Thank you Carcass. That was precisely what was creating confusion as the test cases were not conclusive.

This question is perfectly suited for a strategy called "Looking for Equality" (see video below)
When I see a quantitative comparison question with variables, I ask myself "Are there obvious values that make the two quantities equal?"
Here, the answer is a big YES.

If \(x = 1\), then regardless of the value of k, the two quantities will be equal
So, I already know that the answer will be either C or D.

From this point it's just a matter of testing another set of values.
For example, if \(x = 10\) and \(k = 2\), then we get:
QUANTITY A: \(\frac{x^{2k}}{x^4 } = \frac{10^{4}}{10^4} = 1\)

QUANTITY B: \(x^{\frac{k}{2}} = 10^{\frac{2}{2}} = 10^1 = 10\)

Here Quantity B is greater

Answer: D

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