  There are two notions of exponent of finite-dimensional Hopf algebras
introduced and studied in the literature. In this note, we discuss and compare
their properties including invariance and finiteness in this note.
Specifically, one notion is invariant under twisting and taking the Drinfeld
double, just like the other one. We also find that if the non-cosemisimplicity
and dual Chevalley property hold, both exponents are infinite in characteristic
$0$ but finite in positive characteristic.
