Nezávislým
Nezávislým is a Czech adjective meaning independent. It is the instrumental singular masculine/neuter form of the adjective nezávislý. This grammatical case is often used to express means, manner, or accompaniment. In common usage, "nezávislým" would appear in a sentence describing something or someone acting or existing in an independent manner, or being the means by which something else is achieved independently.
For example, a phrase like "jednat nezávislým způsobem" translates to "to act in an independent manner." Similarly,
The root of the word lies in "záviset," meaning "to depend." The prefix "ne-" negates this, thus