One movement runs through this root: going out. Go out yourself (לָצֵאת); make something go out and you bring it out, remove it, even publish it (לְהוֹצִיא); send goods out across a border and you export (לְיַצֵּא). What comes out is the outcome, and indeed תּוֹצָאָה, "result", is literally "the thing brought out". The initial י drops in the verb but the nouns reveal it. Every word here is verified against pealim, niqqud included.
The same root runs through the verb system. Each binyan is a voice: it bends the one idea into active, passive, causative or reciprocal. Tap to hear.
Three binyanim, one direction outward. The pa'al is you going out; the hif'il is the causative, making something come out (and so "to publish", להוציא לאור, literally to bring into the light); the pi'el specialized into commerce, sending goods out as exports. The passive partners are not lexicalized for daily use.
Same root letters, different noun moulds (mishkalim). The mould tells you the function: who does it, the act of doing it, or the thing produced.
Strip the prefixes, suffixes and vowels. Three consonants remain, and the meaning lives there.