For what value of b does (1/12) ^2b x 12^-2b+2=12

-1/2

-1/4

1/4

no solution

The answer

first, the main properties are:

a^ - p = 1 / a^p

1 ^ b = 1, for all value of b

for solving the problem, we only apply the properties, that is

(1/12) ^2b x 12^-2b+2 = (1/12) ^2b/12^2b + 2 = [ (1/12) ^2/12^2]^b + 2 = 12

[1]^b + 2 = 12, finally 1 + 2 = 12, impossible

so the answer is no solution