carefree
The word means unhindered, free to act, not impeded or burdened. There are no "encumbrances" (literally weights, loads) that impede or prevent an action. This is often metaphorical, as in someone unencumbered by financial problems or unencumbered by legal or moral considerations.
unencumbered
That is the correct spelling of the adjective "unencumbered" (not hindered).
the operating space
A single father would not be considered to be unencumbered unless his children were totally taken care for by his ex-wife. If he had custody of the children, he would be considered encumbered.
plain, unencumbered, clean, casual
He is unencumbered by familial ties. He is family-free!
Invisisble College. or the Human mind.
Any sea dwelling creature possessing unencumbered mobility.
This means unencumbered by responsibilities and able to be directed by one's own imagination.
It was pretty bare and unencumbered by scenery. Modern productions of the plays tend to look the same way.
The word "unladen" refers to being unburdened by weight or unencumbered. It is the opposite of "laden" which would mean a heavy load or a large quantity of something.