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((0.3)^(1/3)(1/27)^(1/4)(9)^(1/6)(0.81)^...

`((0.3)^(1/3)(1/27)^(1/4)(9)^(1/6)(0.81)^(2/3))/((0.9)^(2/3)(3)^(-1/2)(243)^(-1/4))=`

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Solve the followings : The value of the expression ((0.3)^(1//3).(1/27)^(1//4) . (9)^(1//6).(0.81)^(2//3))/((0.9)^(2//3) . (3)^(-1//2) . (1/3)^(-2). (243)^(-1//4)) is :

{(81)^(-3/4)xx((16)^(1/4))/(6^(-2))xx(1/27)^(-4/3)}^(1/3)=

(1)/(3)-(1)/(2).(1)/(9)+(1)/(3).(1)/(27)-(1)/(4).(1)/(81)+….oo=

(1)/(3)-(1)/(2).(1)/(9)+(1)/(3).(1)/(27)-(1)/(4).(1)/(81)+….oo=

9^(3/2)+3xx4^(0)-((1)/(81))^(-1/2)

((16)^((1)/(4)))/((27)^((1)/(3)))+((625)^((1)/(4)))/((81)^((1)/(4)))-(1)/((243)^((1)/(5)))=2

3^((1)/(9)).9^((1)/(27)).27^((1)/(81)).81^((1)/(243))….oo=

(2)/(1).(1)/(3)+(3)/(2).(1)/(9)+(4)/(3).(1)/(27)+(5)/(4).(1)/(81)+…oo=