How do prokaryotes produce ribosomes without a nucleus?

Prokaryotes have 70S(it is measure in centrifuge) ribosomes, each consisting of a small (30S) and a large (50S) subunit and each sub-units have different proteins and RNA's in too groups

In the nuclear region they contain their own circular shaped DNA and RNA segments called "bacterial chromosomes". This contains instructions on how to make essential ribosomes. The ribosomes float freely in the cytoplasm of the prokaryotic cell.

They  reproduce by a process that is called binary fission. The  DNA in such cells is contained in a single circular chromosome called a plasmid within the cytoplasm. The reproductive process starts with the replication of the chromosome. The new chromosome attaches itself to the plasma membrane and the two chromosomes migrate to opposite ends of the cell. The plasma membrane in the middle of the cell grows inward until it closes to separate the cell into two compartments, each with a full complement of genetic material. The cell then "fission" at the center, forming two new daughter cells.