Organisms are classified as either a prokaryote or a eukaryote based on their

The classification of organisms as either a prokaryote or a eukaryote is based on the structure of the organism's cell nucleus

Explanation:

The etymology of the word 'karyote' in both 'prokaryote' and 'eukaryote', is derived from a Greek word that explains the nucleus.

An organism having a true nucleus (i.e a nucleus surrounded by a nuclear membrane) in its cell(s), is classified as a eukaryote.

'Eu' in the word 'eukaryote', is derived from a Greek word that means 'true'.

A prokaryote is an organism that lacks a definite nucleus, hence, having its genetic materials suspended freely in the cyoplasm without a special nuclear membrane enclosing it, aside from its plasma membrane.

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