Single-celled organisms that do not have a membrane-bound nucleus are called prokaryotes.

Here's why:

* Prokaryotes are a domain of life that includes bacteria and archaea. They are characterized by the absence of a membrane-bound nucleus and other membrane-bound organelles.

* Eukaryotes, on the other hand, are organisms that do have a membrane-bound nucleus and other organelles. They include plants, animals, fungi, and protists.

So, the key distinction between prokaryotes and eukaryotes is the presence or absence of a nucleus.