Final answer:
ATP synthase is located in the inner membrane of mitochondria in eukaryotic cells, the plasma membrane in prokaryotic cells, and in thylakoids within chloroplasts in plant cells.
Step-by-step explanation:
To find ATP synthase in a cell, one would look at specific locations depending on the type of cell. In eukaryotic cells, ATP synthase is located in the inner membrane of mitochondria, specifically embedded in the membrane folds known as cristae. Here, ATP synthase plays a crucial role in cellular respiration by utilizing the electrochemical gradient of protons. For prokaryotic cells, ATP synthase is found in the plasma membrane. In the context of photosynthesis, ATP synthase is present in thylakoids within the chloroplasts of plant cells where it facilitates the synthesis of ATP during the light-dependent reactions.