This is the 6195th most frequent Russian word.
техническим
Technical.
The word 'техническим' functions as an adjective (instrumental case) describing 'совершенством' indicating its excellence in a technical domain.
Этот проект обладает техническим совершенством.
This project possesses technical perfection.
The word 'техническим' acts as an adjective (instrumental case) accompanying 'оборудованием' to specify its technical nature.
Мы пользуемся техническим оборудованием каждый день.
We use technical equipment every day.
Here, 'техническим' serves as an adjective (instrumental case) modifying 'состоянием', delineating its relation to the equipment's state.