I'm not sure there's a way to "show it off" really. There's demonstration, which will always have the risk of looking like making shit up, and there's showing off which will always look like waving your dick around.
Roleplay events affect people differently; Some characters might gradually open up as they become more confident, while others might slowly close themselves off in the face of the constant trials and tribulations that comes from being an adventurer. I suppose that's my answer then: You show off experience when you look at someone's growth arc over a period of time and see how they changed with the events that took place.
This is impossible with randoms.
Roleplay events affect people differently; Some characters might gradually open up as they become more confident, while others might slowly close themselves off in the face of the constant trials and tribulations that comes from being an adventurer. I suppose that's my answer then: You show off experience when you look at someone's growth arc over a period of time and see how they changed with the events that took place.
This is impossible with randoms.