(1/36)^n = 216
Rewrite 36 as 6^2
(1/6^2) ^n = 216
Since 36 is in the denominator, the exponent is negative
(6^-2) ^n = 216
Rewrite 216 as 6^3
(6^-2)^n = 6^3
We know that a^b^c = a^(b*c) so
6^(-2n) = 6^3
Since the bases are the same, the exponents are the same
-2n = 3
Solving for n
n =-3/2
n = -1.5