What is the part of the neuron that conducts nerve impulses away from the cell body?

The correct answer is the axon. 

Axons are long, slender projections of a neuron that conduct nerve impulses away from the cell body to other neurons, muscles, or glands. 

Dendrites, on the other hand, are shorter and more branched projections that receive signals from other neurons and conduct them toward the cell body. 

The synapse is the junction between two neurons where information is transmitted from one neuron to another. The nucleus is the organelle within the cell body that contains genetic material.