If $3^{n} = 27$ , then $3^{n - 2}$ $=$ ?

3

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{1}{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{1}{9}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

9

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $3$
$3^{n - 2} = 3^{n} \times 3^{- 2}$ $[∵ a^{m + n} = a^{m} \times a^{n}]$
$= \frac{3^{n}}{3^{2}}$ $[∵ a^{- m} = \frac{1}{a^{m}}]$
$⟹ 3^{n - 2} = \frac{27}{9}$
Thus, $3^{n - 2} = 3$

Suggest Corrections

Similar questions

\frac{3 \times 27^{n - 1} + 9 \times 3^{3 n - 1}}{8 \times 3^{3 n} - 5 \times 27^{n}}

\frac{3 \times 27^{n + 1} + 9 \times 3^{3 n - 1}}{8 \times 3^{3 n} - 5 \times 27^{n}}

\frac{3 \times 27^{n + 1} + 9 \times 3^{3 n - 1}}{8 \times 3^{3 n} - 5 \times 27^{n}}

C_{0} + \frac{3}{2} . C_{1} + \frac{9}{3} . C_{2} + \frac{27}{4} . C_{3} + . . . . . . . . . . . + \frac{3^{n}}{n + 1} . C_{n} = \frac{4^{n + 1} - 1}{3 (n + 1)}

\frac{3 \times 27^{n + 1} + 9 \times 3^{n - 1}}{8 \times 3^{3 n} - 5 \times 27^{n}}

Join BYJU'S Learning Program