1. The problem is to solve the equation $256 = 2^n$ for $n$. 2. We use the property of exponents that if $a^m = a^n$, then $m = n$ when $a > 0$ and $a \neq 1$. 3. Express 256 as a power of 2: $256 = 2^8$ because $2^8 = 256$. 4. Substitute back into the equation: $2^8 = 2^n$. 5. By the property of equality of exponents, $n = 8$. 6. Therefore, the solution is $\boxed{8}$.