Final answer:
The term for the branching of axon terminals allowing a single neuron to influence multiple cells is 'neuronal branching'. This process involves transmitting signals via neurotransmitters across the synaptic cleft to the dendrites of other neurons or target cells.
Step-by-step explanation:
The term that refers to the branching of axon terminals so that a single nerve cell can synapse with and influence many other cells is called neuronal branching. An axon is a tube-like structure of neurons that extends from the cell body, propagating the signal to the axon terminals. These terminals are involved in the release of neurotransmitters, which are chemical messengers that bridge the gap, known as the synaptic cleft, between the axon terminal and the dendrites of other neurons or target cells. This process of synaptic transmission is crucial to neuronal communication, allowing a single neuron to form connections with many other cells, which is essential for complex brain functions.