Given the equation:

$$
\(2^{16}=16^{n+3}\)
$$


We want to find the value of $n$.

Step 1: Express both sides with the same base
Notice that:

$$
\(16=2^4\)
$$


So,

$$
\(16^{n+3}=\left(2^4\right)^{n+3}=2^{4(n+3)}=2^{4 n+12}\)
$$


Step 2: Set the exponents equal
Since the bases are the same (base 2), the exponents must be equal:

$$
\(16=4 n+12\)
$$


Step 3: Solve for $n$

$$
\(\begin{gathered}
4 n+12=16 \\
4 n=16-12=4 \\
n=\frac{4}{4}=1
\end{gathered}\)
$$


Final answer:

1