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Simplify each of the following : (i)((...

Simplify each of the following :
`(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))`

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`(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^(4xx(5)/(4))xx2^(3xx4/(3)))/(5^(2xx(3)/(2))xx3^(5xx3/(5)))=(2^(5)xx2^(4))/(5^(3)xx3^(3))=(32xx16)/(125xx27)=(512)/(3375)`
`(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)`
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