Termites eat wood, but many do not produce enzymes themselves that will digest the cellulose in the wood. instead, some termites house a complex community of protozoa, bacteria, and archaea that could digest the cellulose. imagine an experiment that fed termites either wood only or wood and antibiotics, and then measured the amount of energy extracted from the wood. if both groups gained equal amounts of energy, which of the conclusions is the most logical

More information is required to completely answer the question. Based on the experiment, feeding one group wood only and the other wood and antibiotics, the conclusion to be drawn is that the bacteria that lives in the gut of termites does not aid in digestion of the cellulose in wood.
Antibiotics only affect bacteria and so would leave the protozoa and the archaea in the gut of the termites. Both groups received the same amount of energy at the end of the experiment so it means that digestion is aided by either the protozoa or archaea and not bacteria.

They both determine the exact age of rocks.