kingdom

How can prokaryotes maintain their lifes? Ans: They feed on organic matters by secreting enzyme to digest them. Absorption occurs after this process. They maintain their lives by binary fission instead of meiosis and mitosis.
Can they carry out photosynthesis? Ans: No, they do not have chloroplasts. They also don't have any large organelles such as mitochondrion and rough endoplasmic reticulum (rough ER) . (This is the model answer for A-level biology)
I hope my writing can help you.

some bacteria are photosynthetic. check the link below. http://en.wikipedia.org/wiki/Bacteriochlorophyll

圖片參考：http://upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Troph_flowchart.svg/401px-Troph_flowchart.svg.png

Bacteria can be:

Heterotroph
A heterotroph (Greek heterone = (an)other and trophe = nutrition) is an organism that requires organic substrates to get its carbon for growth and development.
Autotroph
An autotroph is an organism that produces complex organic compounds from simple molecules and an external source of energy, such as light or chemical reactions of inorganic compounds.
Phototroph
Phototrophs (photo=light, troph=nourishment) or photoautotrophs (photo=light, auto=self, troph=nourishment) are organisms which carry out photosynthesis.
Chemotroph
Chemotrophs are organisms that obtain energy by the oxidation of electron donating molecules in their environments. These molecules can be organic (organotrophs) or inorganic (lithotrophs).
Lithotroph
A lithotroph is an organism which uses an inorganic substrate (usually of mineral origin) to obtain reducing equivalents for use in biosynthesis (e.g. carbon dioxide fixation) or energy conservation via aerobic or anaerobic respiration.