This is the 14725th most frequent German word.
noe
"Noe" is not a standard German word. It may be a misspelling or abbreviation.
In this sentence, 'neue' ('new') is used as an adjective, describing the type of shoes purchased.
Ich habe heute neue Schuhe gekauft.
I bought new shoes today.
Here, 'neue' ('new') is again an adjective, characterizing the car being discussed.
Das neue Auto fährt sehr leise.
The new car drives very quietly.
Once more, 'neues' ('new') is applied as an adjective, modifying the noun 'Haus' ('house').