If 1176=2a3b7c, find a, b and c.

First find out the prime factorisation of 1176.

It can be observed that 1176 can be written as $2^{3} \times 3^{1} \times 7^{2}$.

$1176=2^{3} 3^{1} 7^{2}=2^{a} 3^{b} 7^{c}$

Hence, $a=3, b=1$ and $c=2$.