\begin{align*}
2^{2x} & =256^{\frac{1}{2}} \\
2^{2x} & =(2^8)^{\frac{1}{2}} \\
2^{2x} & =(2^4) \\
2x & = 4 \\
x & = \boxed{2}
\end{align*}
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve for $x$: $2^{2x} = 256^\frac{1}{2}$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
2
Solve for $x$: $2^{2x} = 256^\frac{1}{2}$.
test