7.003. $-\log _{2} \log _{2} \sqrt{\sqrt[4]{2}}$.

Translate the above text into English, keeping the original text's line breaks and format, and output the translation result directly.

7.003. $-\log _{2} \log _{2} \sqrt{\sqrt[4]{2}}$.
Solution.

$$
-\log _{2} \log _{2} \sqrt{\sqrt[4]{2}}=-\log _{2} \log _{2} 2^{\frac{1}{8}}=-\log _{2} \frac{1}{8} \log _{2} 2=-\log _{2} 2^{-3}=3
$$

Answer: 3.