Now my question is that will bitcoin itself become an exchange value without fiat currency in the future? Or will fiat currency always exist to explain?
If bitcoin becomes an exchange value in itself, what then would will we be using in measuring the value for what we're using to make exchange with bitcoin. For example I want to buy a tuber of yam, how do I know the value of that yam tuber in BTC if I don't first get the value in fiat. Well! Honestly, It's really stupid a question to ask just as you sincerely said, because I don't see how we get to agree that 1 full BTC is worth buying this yam tuber or not if it's exchange value isn't measured in something as fiat.
That's not a stupid question.
Did you know that people traded goods with each other long before fiat existed? Livestock, shell, stone, gold, and silver all served as mediums of exchange and ways to measure value before fiat became the norm.
If the market had no fixed unit of value, markets can still determine the value of goods through supply, demand, and agreement between buyer and seller. They don't necessarily need an intermediary unit like the USD.
Bitcoin could absolutely take over fiat's role as a unit of value. But the problem is that governments are unlikely to let that happen, because they could lose much of their control over the economy, as well as their power, if Bitcoin became a widely used unit of account.