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Question
Simplify:
`[ 3 xx 27^( n + 1 ) + 9 xx 3^(3n - 1 )]/[ 8 xx 3^(3n) - 5 xx 27^n ]`
Solution
`[ 3 xx 27^( n + 1 ) + 9 xx 3^(3n - 1 )]/[ 8 xx 3^(3n) - 5 xx 27^n ]`
= `(3xx27^n.27+9xx3^(3n).3^-1)/(8xx(3^3)^n-5xx(3^3)^n)`
= `(27^nxx81+9xx27^n.3^-1)/(8xx27^n-5xx27^n)`
= `(27^n[81+9xx3^-1])/(27^n[8-5])`
= `([81+9xx1/3])/3`
= `[ 81 + 3 ]/3`
= `84/3`
= 28
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