I want to know the authenticity of the following Hadith: "No person's prayers is complete unless he says Takbeer, praises Allah-the Mighty and Sublime and Extols Him, recites of the Qur'an what is easy for him". Is this Hadith reported in Abu Dawood and Hakim?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

The Hadeeth you referred to is authentic; it was reported by Abu Daawood, An-Nasaa-i, and Ibn Maajah. Shaykh Al-Albaani graded it sound. The text of the Hadeeth is as follows:

The Prophet said: “The prayer of anyone is not perfect unless he performs ablution perfectly; he should then utter the Takbeer, and praise Allah, the Exalted, and glorify Him; he should then recite as much of the Quran as he desires. He should then say: “Allaahu Akbar” (Allah is Most Great). Next, he should bow so that all his joints return to their proper places. Then he should say: “Sami’a Allaahu Liman Hamidah” (Allah listens to the one who praises Him) and stand erect. He should then say: “Allaahu Akbar,” and should prostrate himself so that all his joints are completely at rest. Then he should say: “Allaahu Akbar”; he should raise his head (at the end of prostration) till he sits erect. Then he should say: “Allaahu Akbar”; then he should prostrate himself till all his joints return to their proper places. Then he should raise his head and say the Takbeer. When he does so, then his prayer is completed.”

Allah knows best.