Maximising the product of stack sizes from 100 coins

You split $100$ coins into stacks of any sizes you like, and you are paid the product of the stack sizes (stacks of $20$, $20$ and $60$ would pay $24000$). The best possible payout can be written as $a\cdot b^{c}$ with $a$ and $b$ coprime. What are $a$, $b$ and $c$?

$a=4$, $b=3$, $c=32$. Any part of size $5$ or more should be split, since $2(k-2)>k$ for $k\ge5$, and a $4$ is as good as $2+2$. Threes beat twos ($3^2>2^3$), so use as many threes as possible; $100=32\cdot3+4$ gives the maximum $4\cdot3^{32}$.