Find the value of n, when $$3^{-7} \times 3^{(3n + 4)} = \frac{3^{11}}{3^5}$$​​

Correct option is C

Given:

​$$3^{-7} \times 3^{(3n + 4)} = \frac{3^{11}}{3^5}$$​​

Formula Used:

​$$a^m \times a^n = a^{m+n}$$​​

​$$\frac{a^m}{a^n} = a^{m-n}$$​​

Solution:

LHS:

​$$3^{-7} \times 3^{3n + 4} = 3^{(3n + 4 - 7)} = 3^{3n - 3}$$​​

RHS:

​$$\frac{3^{11}}{3^5} = 3^{11 - 5} = 3^6$$​​

Equating powers:

3n - 3 = 6

3n = 9

n = 3