#### Answer

$ x=-4$

#### Work Step by Step

Re-write the given equation as: $2^{-x}=2^4$ $(Because: \ 16=2^4)$
Use the rule power rule: $a^p=a^q$ .
We can see that the base $a=2$ is same on both sides of the equation.
So, the exponents will also be equal.
This implies that $p=q$
Therefore, $2^{-x}=2^{4} \implies x=-4$