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If (9^(n+2) xx (3^(-n/2))^(-2)-27^n)/(3^...

If `(9^(n+2) xx (3^(-n/2))^(-2)-27^n)/(3^(3m)xx2^3xx10)=1/27` prove that m-n=1

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`(9^(n+2) xx (3^(-n/2))^-2 - 27^n)/(3^(3m)xx2^3xx10) = 1/27`
`=>((3^2)^(n+2) xx 3^n - (3^3)^n)/(3^(3m)xx2^3xx10) = 1/3^3`
`=>(3^(2n+4) xx 3^n - 3^(3n))/(3^(3m)xx2^3xx10) = 1/3^3`
`=>(3^(3n+4)*3^3 - 3^(3n)*3^3) = (3^(3m)xx2^3xx10)`
`=>3^(3n+7) - 3^(3n+3) = 3^(3m)xx2^3xx10`
`=>3^(3n+3)(3^4 - 1) = 3^(3m)xx2^3xx10`
`=>3^(3n+3)(80) = 3^(3m)xx2^3xx10`
`=>3^(3n+3)(2^3 xx 10) = 3^(3m)xx2^3xx10`
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