If a step-up transformer increases voltage. Does that mean it increases power?

The most basic rule for any transformer is that the power on one side is equal to the power on the other.

Except it’s not quite, because you always get losses, and the power on the secondary will be a tad less than the primary, but nevertheless the rule is right for a lossless one.

If you do Physics, you’ll have learnt that P=IE (in tech we remember W=AV)

If the power on the secondary is to remain consistent with that on the primary, but the voltage has gone up, then necessarily the current available will be lesser.

You never get more power out than in. Because a bunch of scientists with names like Clausius, Helmholtz, and Carnot came and trampled over that idea in their great big Dr Marten’s boots years ago.

Bloody scientists. Ruining everything since the 1500s.