243)n5 × 32n + 1 9n × 3n − 1 = ?

Question

A. 1

B. 2

C. 9

D. $3^{n}$

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Correct Answer :

C. 9

Given Expression

= \frac{(243)^{\frac{n}{5}} \times 3^{2 n + 1}}{9^{n} \times 3^{n - 1}}

=

\frac{(3^{5})^{\frac{n}{5}} x 3^{2 n + 1}}{(3^{2})^{n} x 3^{n - 1}}

= \frac{(3^{5 \times \frac{n}{5}} \times 3^{2 n + 1})}{(3^{2 n} \times 3^{n - 1})}

=

\frac{3^{n} \times 3^{2 n + 1}}{3^{2 n} x 3^{n - 1}}

=

\frac{3^{(n + 2 n + 1)}}{3^{(2 n + n - 1)}}

=

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

=

3^{(3 n + 1 - 3 n + 1)} = 3^{2} = 9 .