What exponent law have I violated? Given the expression: $b^8(2b)^4$, simplify it.

I multiply $b^8$ and $2b$, which gives $(2b^9)^4.$

$(2b^9)^4 = 16b^{36}$. However this is incorrect. 

The correct answer is to distribute the exponent first like so:
$b^8(2^4b^4) = 16b^{12}$. This makes sense, but I'd like to know why my original approach was incorrect.
You have violated the order of operations.  $b^8 (2b)^4$ means that $2b$ is raised to the fourth power, then multiplied by $b^8$.  If you were to perform multiplication of $b^8$ by $2b$ before you raise to the fourth power, you would also have raised $b^8$ to the fourth power, resulting in an additional factor of $b^{24}$.  As you can see, $36 = 24 + 12$.



To illustrate how one might have written the expression to obtain your erroneous result, we would write instead $(b^8 (2b))^4 = 16b^{36}$.
$b^8(2b)=2b^9$, $b^8(2b)^4=b^82^4b^4=16b^{12}$.