Can anyone explain to me how does roughly 3.3 equal to 3 to the power of 1/3(answer choice d)?

It doesn’t, but I don’t see anything in your screenshot that suggests that Greg did 3.3 = 3^{\frac{1}{3}}.

I think the user is confusing mixed-fraction 3\dfrac{1}{3} = \dfrac{(3\times3)+1}{3}=\dfrac{10}{3} \simeq3.33 as three raise to the power one-third: 3^{\frac{1}{3}}

X value is roughly 3.3 and Greg chose answer d(3 to the power 1/3), which means that he equates 3.3 with 3 to the power 1/3. None of the answer choices is 3.3. The only one close to 3.3 among answer choices is 3. I know that 3.3 is not equal to 3 to the power 1/3 but don’t know why answer choice is 3 to the power 1/3 when X value is roughly 3.3.

That isn’t what the option is though.