This is the 13569th most frequent Polish word.
pisemnego
"Written."
The word 'pisemnego' is used as an adjective modifying 'pozwolenia' to specify the format of the permission.
Uczeń potrzebuje pisemnego pozwolenia od rodzica na wzięcie udziału w wycieczce.
The student needs written permission from a parent to participate in the trip.
Here, 'pisemnego' modifies 'wyjaśnienia', indicating that the explanation should be in written form.
Nie załączono pisemnego wyjaśnienia decyzji.
A written explanation of the decision was not included.
In this sentence, 'pisemnego' qualifies 'zawarcia', emphasizing that the agreement was made in a documented written form.