Answer:
Option (4). 1
Step-by-step explanation:
Given expression is [tex]\frac{(216)^{n-2}}{(\frac{1}{36})^{3n}}[/tex]= 216
[tex]\frac{[(6)^3]^{n-2}}{[(\frac{1}{6})^2]^{3n}}[/tex] = 216
[tex]\frac{(6)^{3(n-2)}}{(\frac{1}{6})^{2\times 3n}}[/tex] = 216
[tex]\frac{(6)^{3(n-2)}}{(6)^{-6n}}[/tex] = 216
[tex]\frac{(6)^{3n-6}}{(6)^{-6n}}[/tex] = 216
[tex](6)^{3n-6}\times (6)^{6n}[/tex] = 216
[tex](6)^{3n-6+6n}[/tex] = [tex](6)^3[/tex]
[tex](6)^{9n-6}=(6)^3[/tex]
9n - 6 = 3
9n = 3 + 6
9n = 9
n = 1
Option (4) will be the answer.
