If `1176=2^a xx\ 3^bxx\ 7^c ,` find the values of `a ,\ b\ a n d\ c` . Hence, compute the value of `2^a xx\ 3^b xx\ 7^(-c)` as a fraction.

Explanation

`1176=2^a×3^b×7^c`
`=>2xx2xx2xx3xx7xx7=2^axx3^bxx7^c`
`=>2^3xx3xx7^2=2^axx3^bxx7^c`
Now by comparing both sides, we get:
`2^3xx3xx7^2=2^axx3^bxx7^c`
`:.a=3`,`b=1`and `c=2`
`=>2^axx3^bxx7^(−c)`
`=>2^3xx3^1xx7^(−2)=24/49`
`therefore` The value of `a=3`, `b=1` and `c=2`
`therefore` The value of `2^axx3^bxx7^c=24/49`