(9^n×3^n×3^2-27^n)/(3^15×2^3)=1/27.Find the value of n

Question

We have to find the value of n. I need the method to do it and answer also

Answer 1

n=4.

Here’s why.

27=3³, 9=3², so the equation can be simplified:

(3^(3n+2)-3^(3n)=2³×3¹².

(3^3n)(9-1)=8×3¹².

3^(3n)=3¹², so 3n=12, n=4.