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### Discussion :: Surds and Indices

1. $$\frac { (243)^n/5*362n+1} { 9^n*3^n-1 }=?$$

2.  A. 1 B. 2 C. 9 D. 3n

Explanation :

Given  Expression=$$\frac { (243)^n/5*362n+1} { 9^n*3^n-1 }$$

=$$\frac {(3)^((n/5)*3^2n+1} { (3^2)^n*3^n-1}$$

=$$\frac {(3)^((n/5)*3^2n+1} { (3^2n*3^n-1)}$$

=$$\frac { 3^n*3^2n+1} {3^2n *3^n-1}$$

=$$\frac { 3(n+2n+1} {3(2n+n-1 }$$

=$$\frac {3^3n+1} { 3^3n-1 }$$

 = 3(3n + 1 - 3n + 1)   = 32   = 9.

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