The accusative case is used to indicate the destination, the final goal of motion (eg. ехать в Италию -- to go to Italy), while the dative with the verb of motion and the preposition ''по'' can be used to denote the process of moving from place to place, moving around, getting around etc. without much reference to destination (''по'' here usually corresponds to the english prepositions ''along'', ''around'' or some others): to travel around Italy -- путешествовать по Италии to get around the city -- гулять по городу walk along the streets — идти по улице walk across the room — ходить по комнате etc. etc.

Hello. "идти по выставке" - we can't use this preposition here, it is incorrect. You can use only "на" and it means that you are going to visit some place ( выставка, конференция (confernce), мероприятие ( event) etc.). So you have intentions to visit something or you are already goung there. But let's take this example: идти по стадиону-идти на стадион. So the second one it is an intention to visit a stadium( or you are in process of going there), but the first one it is a process of going (already) inside this stadium, so you are already there! Идти по дороге - to go on a road ( you are there). "Выходи/Иди на дорогу" - you are are not there , but you are going to be there. The same cases we can dind with "В" and "По": идти в музей ( not yet there), идти по музею ( alredy there, to be in process of seeing pictures in this museum, for example)

идти по is used to talk about a certain surface - идти по улице, по проспекту, по дороге, по площади, мосту. выставка isn't any kind of surface and so it sounds unnatural. however, you can say ходить по выставке, which means that you walk past certain exhinits enjoying yourself:) preposition "на" shows direction.

идти куда? на выставку = они собираются быть там (на выставке) идти где? по выставке = они уже там, гуляют и смотрят выставку Learn Russian online www.babylon-project.com