सरल कीजिए:
(i) `((25)^(3//2)xx(243)^(3//5))/((16)^(5//4)xx(8)^(4//3))`
(ii) `(16xx2^(n+1)-4xx2^(n))/(16xx2^(n+2)-2xx2^(n+2))`

Explanation

(i) `((25)^(3//2)xx(243)^(3//5))/((16)^(5//4)xx(8)^(4//3))`
`=((5^(2))^(3//2)xx(3^(5))^(3//5))/((2^(4))^(5//4)xx(2^(3))^(4//3))=(5^(2xx3//2)xx3^(5xx3//5))/(2^(4xx5//4)xx2^(3xx4//3))=(5^(3xx3^(3)))/(2^(5)xx2^(4))=(125xx27)/(32xx16)=3375/512`
(ii) `(16xx2^(n+1)-4xx2^(n))/(16xx2^(n+2)-2xx2^(n+2))`
`=(2^(4)xx2^(n+1)-2^(2)xx2^(n))/(2^(4)xx2^(n+2)-2xx2^(n+2))=(2^(n+5)-2^(n+2))/(2^(n+6)-2^(n+3))`
`=(2^(n+5)-2^(n+2))/(2.2^(n+5)-2.2^(n+2))=(2^(n+5)-2^(n+2))/(2(2^(n+5)-2^(n+2)))=1/2`