When he was cast out (ektethentos autou). Genitive absolute with first aorist passive participle of ektithēmi.
Took up (aneilato). Second aorist middle indicative (with first aorist vowel a instead of e as often in the Koinéš) of anaireō, common in the N.T. in the sense of take up and make away with, to kill as in Act 7:28, but here only in the N.T. in the original sense of taking up from the ground and with the middle voice (for oneself). Quoted here from Exo 2:5. The word was used of old for picking up exposed children as here. Vincent quotes Aristophanes (Clouds, 531): “I exposed (the child), and some other women, having taken it, adopted (aneileto) it.” Vulgate has sustulit. “Adopted” is the idea here. “After the birth of a child the father took it up to his bosom, if he meant to rear it; otherwise it was doomed to perish” (Hackett).
Nourished him for her own son (anethrepsato auton heautēi eis huion). Literally, “she nursed him up for herself (heautēi besides middle voice) as a son.” This use of eis=as occurs in the old Greek, but is very common in the lxx as a translation of the Hebrew le. The tradition is that she designed Moses for the throne as the Pharaoh had no son (Josephus, Ant. ii. 9, 7).