निम्न में से प्रत्येक को सरल कीजिए।
`((25)^(3//2)xx(243)^(3//5))/((16)^(5//4)xx(8)^(4//3))`

Explanation

`(i)` यहाँ
`((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^(2xx(3)/(2))xx3^(5xx(3)/(5)))/(2^(4xx(5)/(4))xx2^(3xx(4)/(3)))`
`=(5^(3)xx3^(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)-2^(1)xx2^(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)`