Like in every similar position (e.g. sports trainers, preachers, band leaders, ...) teachers are both powerless and powerful at the same time. If the student has respect for them/their role the power can be real, if we are talking about students who question the rules (and have parents that don't care/actively support the breaking of them) teachers are powerless.

Is a babysitter powerful? Towards an adult no, towards the child yes. Towards a certain type of child, no.