When I was sentence mining, I found the following sentence:
Could someone explain how 出さず was conjugated from 出す?
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The ず-form of a verb V is usually translated as "without doing V". In that sense, it has a similar meaning to Vないで.
It is formed by taking the ない-form stem, but instead of adding ない, you add ず.
So, here: 出す (dict.f.) → 出さない (nai-f.) → 出さ (nai-f. stem) → 出さず (zu-f.).
From what I understand, it's a hangover of a negative form used more commonly in classical Japanese. In modern Japanese, it is mainly used in writing, rather than speech, where Vないで would be preferred.
Hope that helps!