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

Explanation

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