if 9n xx 35 27 3 3 81 4 27 then, Surds and Indices, General Mathematics

Question:If` (9^n xx 3^5 xx (27)^3)/(3 xx (81)^4) = 27`, then, n equals :

A 0 
B 2 
C 3 
D 4

/35

+ AnswerC

+ Explanation`(9^n xx 3^5 xx (27)^3)/(3 xx (81)^4)`

`= 27 => (3^2n xx 3^5 xx (3^3)^3)/(3 xx (3^4)^4`

`= 3^3`

`= (3^2n xx 3^5 xx 3^9)/(3^1 xx 3^16)`

`= 3^3 or 3^(2n + 5 + 9)`

`= 3^3 xx 3^1 xx 3^16 or 3^(2n + 14)`

`= 3^20

`:. 2n + 14`

`= 20 or 2n`

`= 6 or n = 3`

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