`a)` `(2^7 . 27^2)/(16^2 . 81)=(2^7 . 3^6)/(2^8 . 3^4) =(3²)/2 = 9/2`
`b)` `(3^12 . 27^10)/(9^22)=(3^12 . 3^30)/(3^44) =3^42/3^44 = 1/(3²)=1/9`
`c)` `(3^17 . 27^11)/(9^24)=(3^17 . 3^33)/(3^48) =3^50/3^48 =3²=9`
`d)` `(3^17 . 81^11)/(27^10 . 9^15)=(3^17 . 3^44)/(3^30 . 3^30) =3^61/3^60 = 3`
`e)` `(9². 2^11)/(16² . 6³)=(3^4 . 2^11)/(2^8 . 2³ .3³) =(3^4 . 2^11)/(2^11 . 3³) = 3`
`f)` `(2^10 . 3^31 + 2^40 . 3^6)/(2^11 . 3^31 + 2^41 . 3^6)=(2^10. 3^6 .(3^25 + 2^30))/(2^11. 3^6 .(3^25 + 2^30))= 2^10/2^11 = 1/2`