Can you leave the blowdryer or flat iron plugged in?
It is always recommended you unplug all appliances given electricity always transfers when an item is plugged in. At a minimum, never leave these items on and unsupervised and make sure you only plug bathroom appliances into a GFI certified plug. This will cause the plug to shutdown if there is a surge or short. Remember to ALWAYS turn off all appliances when they are not in use.