The Bard levels do not stack and you have to keep track of both abilities/pools separately.
Inspiring Prowess does not say that it stacks with Bard levels:
Inspiring Prowess (Ex): At 3rd level, an exemplar gains the ability to
use certain bardic performances. She can use this ability for a number
of rounds per day equal to 3 + her Charisma modifier; this increases
by 1 round per brawler level thereafter. The exemplar’s effective bard
level for this ability is equal to her brawler level – 2. At 3rd
level, the exemplar can use inspire courage. At 11th level, the
exemplar can use inspire greatness. At 15th level, the exemplar can
use inspire heroics. Instead of the Perform skill, she activates this
ability with impressive flourishes and displays of martial talent
(this uses visual components). This ability otherwise functions as
bardic performance; feats and other effects that affect bardic
performance (such as the Extra Performance feat) apply to it. This
ability replaces maneuver training and AC bonus.
But in order to stack, abilities need to specifically call out that they stack, as per this FAQ:
Channel Energy: If I have this ability from more than one class, do they stack?
No — unless an ability specifically says it stacks with
similar abilities (such as an assassin's sneak attack), or adds in
some way based on the character's total class levels (such as improved
uncanny dodge), the abilities don't stack and you have to use them
separately. Therefore, cleric channeling doesn't stack with paladin
channeling, necromancer channeling, oracle of life channeling, and so