Final answer:
Active transport of ions across the membrane using the Na+/K+ pump, which requires ATP, restores the ion gradients after an action potential.
Step-by-step explanation:
The activity that restores the ion gradients across the plasma membrane of an axon after an action potential has occurred is active transport of ions across the membrane. This is an energetically unfavorable process that requires energy, usually from the hydrolysis of ATP. The Na+/K+ pump, an integral protein that functions as a pump in active transport, actively moves Na+ ions out of the cell and K+ ions into the cell against their respective concentration gradients. This ensures that the cell can maintain the ion gradients necessary for generating the action potential, even after firing hundreds of times in rapid succession.