We notice that $16 = 2^4$, so we can rewrite the equation as $2^{64} + 2^{64} + 2^{64} + 2^{64} = 2^x$.
Simplifying, we get $4 \cdot 2^{64} = 2^x$.
Since $2^{64}$ is equal to $2^{64} \cdot 1$, we can rewrite the equation as $4 \cdot 2^{64} \cdot 1 = 2^x$.
Using the properties of exponents, we know that $a^m \cdot a^n = a^{m+n}$, so we can simplify the equation to $2^{64+2} = 2^x$.
Therefore, $64+2=x$ and $x=\boxed{66}$.
The answer is: 66
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Determine the value of $x$ in the equation $16^{16} + 16^{16} + 16^{16} + 16^{16} = 2^x$.

### Answer:
