Surds and Indices - Arithmetic Aptitude Questions and Answers

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

3ⁿ

Answer : Option C

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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