My second to last short phrase exercise in Introduction to Attic Greek, page 153, had me writing, “It will be possible.”
I had to give up and just look at the future tense from the chart in Unit 9.
The answer is ἐξέσται. I do not know why the accent shifted to the second epsilon, as the present form is ἔξεστι.
Is there some contraction that went on?
Perhaps it is just combining ἐκ with ἔσται?
It seems to be breaking the recessive rule.
On page 150
“Note the elimination of theme vowel ε in the third person singular, ἔσται, not *ἔσεται. Because of the loss of this syllable, the compounds are also accented on the penult in this inflection: παρέσται, ἀπέσται, ἐξέσται.”
So when the theme vowel dropped, the first syllable moved over to its place, and then ἐξ did not affect eh accent?
Probert says (New short guide to the accentuation of Ancient Greek)
“The third person singular future indicative of the verb “to be” oddly retains its accent on the penultimate syllable in compounds. The reason for this accent is not clear; the influence of the (Homeric) form παρέσσται may be involved. For discussion see Lejeune, Remarques, p. 65.”
If Probert can’t give a simple explanation I am not going to try. Unless enlightenment comes from Hylander or mwh I suggest just learning it and moving on.
ευχαριστώ!
I took German about 30 years ago and forgot almost all of it. One thing I remember in grammar classes is that sometimes things are a certain way just because that is the way it is. 
Better:
εὐχαριστῶ
Yes, and at the beginning level it’s sometimes better to take it on faith, and worry about the “why” of things after you’ve absorbed a bit more of the language.
https://babel.hathitrust.org/cgi/pt?id=mdp.39015004180645&view=1up&seq=289
See the sentence beginning on page 275: “Unum hujusmodi sermonem…” You’ll find some ancient sources on the accentuation. They pretty much say the same as Mastronarde, though the logical chain is presented as going in the other direction.
Probert’s quoted remark (which I don’t have access to right now), makes me think that Lejeune disputed this reasoning.