668 - ～ぬく
JLPT N2: ～ぬく (completely; thoroughly; to the end)
～ぬく can be added to the ます-stem of VERBS when we want to say "VERB completely," "VERB thoroughly," "VERB to the end," and so on.
In isolation, the verb 抜く (ぬく) means something like "to extract," "to pull out," or "to omit."
I'm not entirely sure why the meaning changes to "do something until the end" or "do something thoroughly" when attached to other verbs.
なんど も ざせつ しかけた けれど、 なんとか この けんきゅう を やりぬく こと が できました。
I almost gave up a number of times, but in the end I somehow managed to complete this research.
Literally: “many times over (=how many times + も) + (giving up or feeling frustrated due to a) failure / setback + almost did + but, + somehow + this + research + を + carry out / finish / complete + thing + が + was able to do.”
やる, "to do."
やりぬく, "to carry out to completion," "to accomplish," "to do all the way."
Note the formation:
ます ＋ ぬく
To be honest, I'm not sure if teaching ～ぬく as a grammar point is a good idea. If you go around attaching it to the ます-stem of random verbs, there's a good chance that you're going to say something strange-sounding.
Instead, I would just learn some of the common "VERB-ぬく" combos. In this lesson, we have:
生きる（いきる // to live; to exist）
↓ ↓ ↓
生き抜く（いきぬく // to survive; to live through）
知る（しる // to know）
↓ ↓ ↓
知り抜く（しりぬく // to know thoroughly）
考える（かんがえる // to think about; to consider）
↓ ↓ ↓
考え抜く（かんがえぬく // to thoroughly consider ）
All of these are common enough that they have their own entries in the dictionary.
Well, let's see these in some examples...
ロシア の のらいぬ は かこくな かんきょう で いきぬく ために、 ちかてつ を のりこなす など、 げきてきな しんか を とげた。
In order to survive in such a harsh environment, stray dogs in Russia have developed dramatically, learning how to do things like ride the subway.
Literally: “Russia + の + stray dog + は + harsh + environment + で + survive / live through + in order to, + subway + を + manage to ride / master riding + and so on, + dramatic + development / evolution + を + accomplished / achieved.”
むかし から モテモテ だった ダリル は、 おんなごころ を しりぬいている。
Darryl, who has always been popular with girls, just (completely) understands women.
Literally: “a long time ago + from / since + popular (with the opposite sex) + was + Darryl + は, + woman’s heart / female psychology + を + is knowing thoroughly.”
かんがえぬいた けっか、 びじゅつ の せんもんがっこう に いく ことにした。
After thinking it through, I’ve decided to go to an art institute.
Literally: “thought thoroughly + result, + art + の + technical school + に + decided to go (=go + thing + に + did).”
I recommend going over these somewhat similar grammar points that we've covered before: