Question

How you could use a microscope to determine if a simple was either a prokaryote or a eukaryote

Answer 1

You could check if their cells had a nucleus or not. If it did it would be a eukaryote, if it did not then it would be a prokaryote.

Answer 2

Defined as pre-nucleus, prokaryotes are cells that contain no membrane-based organelles, including a nucleus.

Mostly recognized as bacteria, two prokaryotic kingdoms exist: Monera or Bacteria and Archaea.

Seemingly simple in structure and markedly different from eukaryotic and protist organisms, many scientists believe prokaryotic cells were amongst the first on the Earth and very well may out-survive all other organisms.

http://www.microscopemaster.com/prokaryotes.html