Final answer:
Kingdoms Plantae and Animalia have nucleus-containing eukaryotic cells, unlike Archaebacteria (Archaea) and Bacteria, which are prokaryotes without a nucleus.
Step-by-step explanation:
Kingdoms Plantae and Animalia have cells with a nucleus. Kingdoms Archaebacteria (now often referred to as Archaea) and Bacteria consist of prokaryotic cells, which do not have a nucleus.
The kingdoms that have a nucleus are Plantae and Animalia.
In biological classifications, organisms are grouped based on various characteristics, including cell structure. Two broad categories of cell types exist: eukaryotic and prokaryotic. Eukaryotic cells contain a nucleus and other membrane-bound organelles. The kingdoms that fall under the eukaryotic category are Plantae, which includes all plants, and Animalia, which includes all animals. Both these kingdoms are part of the domain Eukarya, which is characterized by cells with a distinct nucleus. Conversely, Archaebacteria (or Archaea) and Bacteria are part of the prokaryote category and do not have a nucleus.
Cells within these kingdoms lack a bounded nucleus and other membrane-bound organelles. This distinct difference is what sets apart eukaryotic organisms from prokaryotic organisms. The classification system that encompasses this is a relatively modern concept, introduced by Carl Woese and colleagues in the 1970s. It is based on the genetic and biochemical distinctiveness observed in the fundamental structures of cells and their ribosomal RNA, leading to the establishment of the three-domain system of Bacteria, Archaea, and Eukarya.