Can I pump my MTB tire to max (55 psi / 380 kPa) without the tube inside bursting? I have a e-mountain bike and I use to commute to uni every day. I have heard that higher tire pressures give you a bit more speed. My tires say I can pump to 55 psi (380 kPa) but I don't know if my tube can handle the same pressure. Don't want to buy a new tube. I currently have them at 40 psi (280 kPa). Will 47 to 50 psi (320–380 kPa) burst my tubes?
It can't burst the tube, because the tube is completely surrounded by the tyre and rim.

Bear in mind, though, that higher pressures don't automatically mean a faster ride. There are two competing factors: a soft tyre is constantly losing energy due to being squashed flat against the road, but a hard tyre loses energy because any bumps you go over have to lift the whole bike, instead of just deforming the tyre.  I don't ride mountain bikes so I don't know where that trade-off starts to bite.

On an e-bike, I'm not sure this will make much difference, though: it just means that the assist motor will have to work less hard at any given speed.