Following repolarization, the neuron may become slightly hyperpolarized before it re-establishes its resting membrane potential. Hyperpolarization is due to a difference between how the voltage-gated Na+ and K+ channels work. What is this difference?

Membrane potential represents charge difference across the membrane, all biological cells are negative inside (cytoplasm) and positive outside (due to difference in ionic distribution)
In a typical neuron cell membrane potential of cytoplasm is negative at rest (when no stimulus is applied) hence called resting membrane potential
Resting membrane potential of excitable cells is established by Na+ and K+pump
Repolarization starts with the efflux of K+ by the opening of voltage gated K+ channels
Voltage gated K+ channels starts to open when voltage gated Na+ channels becomes inactive
Hyperpolarization occurs due to excessive efflux of K+ by voltage gated K+ channels
Additional efflux of K+ occurs due to slow inactivation of voltage gated K+ channels