The president exercise all the power only on the advice of the council of ministers explain

Because India is a parliamentary executive.
Meaning , executive is dependent on the support of parliament, the moment it looses support it looses satta (government)
Now coming to the point why the president’s is bound by the advice given by the council of ministers. : because as already mentioned above we are a “parliamentary executive” , the executive is accountable to parliament, and parliament is accountable to public. So that means executive is indirectly accountable to public for all its actions. Thats why the advice was made binding. Since our constitution makers did not want to vest all the authorities on a single person (in this case president) unlike unites states hence that advice was made binding .