soundly
In a deep, complete, or very thorough way.
Soundly means deeply, thoroughly, or completely. When you sleep soundly, you're in such a deep sleep that noises and movements barely disturb you. After a long day of hiking and swimming, you might fall asleep the moment your head hits the pillow and sleep soundly all night.
The word also describes doing something in a convincing or decisive way. When one team defeats another soundly, they don't just barely win: they dominate the game from start to finish. A basketball team that wins 98 to 52 has won soundly. When someone is soundly criticized, the criticism is thorough and harsh, leaving little room for argument.
You might also hear that something is built soundly or soundly constructed, meaning it's made well and will hold up over time. A soundly built treehouse won't wobble or creak because every board is secure and every nail is driven in properly.