What is the classification of bacteria that do not have a nucleus?

Bacteria are classified as prokaryotic organisms, which are characterized by the absence of a true nucleus and membrane-bound organelles. Prokaryotic cells typically have a simpler structure compared to eukaryotic cells, which do have a nucleus. The lack of a nucleus means that the genetic material in prokaryotes is not enclosed within a membrane but instead is located in a region called the nucleoid.

In the context of cellular classification, eukaryotic organisms include all cells that have a nucleus, such as plants, animals, and fungi. Multicellular and unicellular refer to the number of cells in an organism – multicellular organisms are made up of many cells, while unicellular organisms consist of just one cell. While bacteria are indeed unicellular, the defining factor for their classification is their prokaryotic nature, making "prokaryotic" the correct answer.