Practice | Hashtable

Home > Practice > Arithmetic Aptitude > Surds and Indices > Miscellaneous

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

A. 1

B. 2

C. 9

D. 3ⁿ

Solution:

\begin{aligned} Given Expression \\ = \frac{{(243)}^{n / 5} \times 3^{2 n + 1}}{9^{n} \times 3^{n - 1}} \\ = \frac{{(3^{5})}^{n / 5} \times 3^{2 n + 1}}{{(3^{2})}^{n} \times 3^{n - 1}} \\ = \frac{(3^{5 \times (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} \times 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 \end{aligned}

You must login to add comments. Login now.