Exegesis:
ēdē de kai. de kai is best understood as giving special emphasis to ēdē ‘already,’ in order to make clear that John’s call is urgent.
hē axinē ‘axe.’
pros tēn rizan tōn dendrōn keitai ‘is lying at, or, directed towards, the root of the trees,’ cf. Plummer. pros with accusative suggests movement or direction, which, in the present context, because of keitai ‘is lying,’ means a movement which has come to rest, or a direction in which the axe points. Weiss thinks that the clause refers, to the moment immediately before the first blow, when the woodman puts his axe at the very place where it has to come down later. This interpretation is preferable.
riza (also 8.13) ‘root.’
dendron ‘tree.’ Here and in 6.43f used in connexion with the picture of the tree and its fruits.
oun ‘then,’ indicating that what follows in and inference from the preceding.
mē poioun karpon kalon ‘that does not bear good fruit.’ The use of mē with the participial phrase indicates that is has conditional force: every tree will be cut out, if it does not bear good fruit. The expression is the same as in v. 8 but here it is used in a literal sense.
kalos “beautiful”, as indication of quality, ‘good.’ The good fruit to which John refers, is the fruits that befit repentance of v. 8.
ekkoptetai ‘is cut down,’ but the present tense may well have futuristic meaning, since the context is prophetic.
eis pur balletai ‘is thrown into the fire.’ For the present tense cf. preceding note. The fire is the fire of judgment, as often in the Old Testament, cf. Jer. 11.16; 21.14; 22.7; Ezek 15.6f, and “the unquenchable fire” in v. 17.
Translation:
The verse takes up the expression ‘bear fruits’ from v. 8a, but now in a living and rather elaborate metaphor. If the underlying comparison of fruit trees with human beings has been made explicit in v. 8a (which see), the metaphor will be easily understood here: if not, it may be advisable to add such an explicit reference here, cf. ‘You are like trees. The axe…’ (Manobo).
The axe is laid to, or, “the axe lies ready at” (The Four Gospels – a New Translation, similarly Bahasa Indonesia), ‘the axe is ready to cut’ (Kekchi, where a literal rendering would suggest that the axe had accidentally been left at the foot of the tree), ‘the axe is-used-to-menace’ (Balinese). If idiom requires a personal agent, one may say, ‘some one is taking the axe towards (or, swings the axe against) the tree’; where an axe or comparable instrument is unknown the rendering of the sentence will have to become something like, ‘the moment is near that the trees will be cut down, or that some one will cause the trees to come down.’ In Zarma one does not say ‘to cut down a tree’ but ‘to kill a tree.’
Root. If a literal rendering would suggest something low down in the soil, the word can better be rendered, ‘base’ (Malay; similarly Ekari, which uses a word that also can refer to the back end of a boat), ‘foot’ (Manobo); Batak Toba can use here a specific term for roots that have grown so big and thick as to be visible.
Thrown into the fire, or, ‘lost/consumed in fire’ (Pohnpeian), or ‘burnt with/in the fire.’ One version simply had ‘is-burnt,’ but a reference to ‘the fire’ should preferably be preserved because of the specific meaning the term has in this context.
Quoted with permission from Reiling, J. and Swellengrebel, J.L. A Handbook on the Gospel of Luke. (UBS Handbook Series). New York: UBS, 1971. For this and other handbooks for translators see here . Make sure to also consult the Handbook on the Gospel of Mark for parallel or similar verses.