You have the following equation:
(6²)ˣ = 1
In order to determine what is the possible value of x, you consider the following expression:
a⁰ = 1
which means that any number exponentiated to zero equals to 1.
Then, in the given equation (6²)ˣ = 1, you can conclude that x must be equal to zero because it is the only way that the equation has a valid solution. In fact:
(6²)⁰ = 1
Hence, x = 0
In the second case, that is, for (6⁰)ˣ = 1, you take into account that the exponent must be multiplied. Thus, you have 6⁰ˣ = 1. Any number multiplied by 0 equals 0. Then, the solution for this equation are all real numbers.
x = (-∞ , ∞)
