Between this and your prior question it really looks like you are just posting your homework here for us to do for you. Please edit your post to give us a sense of your efforts. What have you tried? Where are you getting stuck? — lulu18 hours ago
@MikeMiller @Lord_Farin: This post does not answer the question (which explicitly states that it is about definability and is asking how to do it for variable exponents since fixed exponents can easily be done).
@XanderHenderson I disagree; and besides, that information, in the dupe, is clarified further for the case of the asker, who likely meant, but simply didn't know how to format, $a^{b^c}$, so wrote $a^b^c$.
@amWhy I try not to infer what the asker wants, aside from what is written. They write 2^3^4, which is ambiguous in a way that $2^{3^4}$ is not. If the asker were to clarify that they just didn't know how to format the mathematics, then I would agree with you. As it is, there is a clearly phrased question about the (bad) notation a^b^c.
It should also be noted that the asker only "kinda" has their question answered:
Thanks for all the links and comments, they kinda solved my confusion — Spectra19 mins ago
I've made two distinct points: (1) the question is, as written, is about the notation a^b^c, and not about the notation $a^{b^c}$. One can argue that this is because the asker didn't know how to format the mathematics, but such an argument requires reading more into the question than is written. (2) The asker's question is not answered by the older question, which implies that the older question is not addressing the same issue.
They really don't look that similar to me... Even looking at the original version of the older question, the exponential expressions were formatted in a more readable way. In any event, I've left a comment asking for clarification from the asker of the newer question.
Ah, nevermind. The asker replied, and indicated that they just didn't know how to format the math.
@Shaun Indeed. It's now closed, and need only one more delete vote. I also flagged it for moderator attention as "trolling".
Unlikely that many of you are around, but @user21820, @Did, @MikeMiller, @MartinR Please help in the deletion of this nonsense post from a troll. Only one more delete vote is needed.
@amWhy Voted to close and I've flagged it for a moderator, saying the user is posting a lot of nonsense - I don't know what they'll do about it but maybe they could have a word with the user or something.
@Shaun Thanks; ditto on my end: voted to close, and flagged for mod attention.
Unfortunately, it happens to be Christmas Eve, a good time for trolls to attack, because anyone can reasonably figure most mods will likely not be around much, due to their false assumption that "things will be slow" and "uneventful".