Simplify each of the following: `(a)\ (7^n-3\ xx\ 7^(n+1))/(20\ xx\ 7^n-2\ xx\ 7^n)` ` (b)\ (5^n-6\ xx\ 5^(n+1))/(9\ xx\ 5^n-2^2xx\ 5^n)` `(c)\ (16\ xx\ 2^(n+1)-4\ xx\ 2^n)/(16\ xx\ 2^(n+2)-2\ xx\ 2^(n+2))`

Explanation

Given that:
`(1.) (7^n-3\ xx\ 7^(n+1))/(20\ xx\ 7^n-2\ xx\ 7^n)`
Using
`a^m+n=a^m xx a^n`
`=(7^n - 3 xx 7^n xx 7^n) / 20 x 7^n - 2 xx 7^n`
`=7^n(1- 3 xx 7) / 7^n(20-2)`
`=-20/18`
`=-10/9`
`(2.) (5^n-6\ xx\ 5^(n+1))/(9\ xx\ 5^n-2^2xx\ 5^n)`
`=5^n - 6^n xx 5^n xx 5^1/9 xx 5^4 - 4 xx 5^4`
`=5^n(1-6 xx 5)/5^n(9-4)`
`=-29/5`
`(3.)(16\ xx\ 2^(n+1)-4\ xx\ 2^n)/(16\ xx\ 2^(n+2)-2\ xx\ 2^(n+2))`
`=16 xx 2^n xx 2 - 4 xx 2^n/16 xx 2^n xx 2^2 -2xx 2^n xx 2`
`=2^n(16 xx 2 -4)/2^n(16 xx 4 -2 xx 4)`
`=32-4/64-8`
`= 28/56`
Hence the required answers are `-10/9`,`-29/5`,`28/56`