Niklas takes a dose of $25$ micrograms $(\text{mcg})$ of a certain supplement each day. The supplement has a half life of $4$ hours, meaning that $\dfrac{1}{64}$ of the supplement remains in the body after each day.
**How much of the supplement is in Niklas's body immediately *after* the $12^\text{th}$ dose?**
*Round your final answer to the nearest hundredth.*
[[☃ numeric-input 1]] $\text{mcg}$