Question

For what value of n does

Answer 1

Option (4). 1

Explanation:

Given expression is
`((216)^(n-2))/(((1)/(36))^(3n))`= 216

`([(6)^3]^(n-2))/([((1)/(6))^2]^(3n))` = 216

`((6)^(3(n-2)))/(((1)/(6))^(2* 3n))` = 216

`((6)^(3(n-2)))/((6)^(-6n))` = 216

`((6)^(3n-6))/((6)^(-6n))` = 216

`(6)^(3n-6)* (6)^(6n)` = 216

`(6)^(3n-6+6n)` =
`(6)^3`

`(6)^(9n-6)=(6)^3`

9n - 6 = 3

9n = 3 + 6

9n = 9

n = 1

Option (4) will be the answer.