This is the 2816th most frequent Russian word.
славянский
"Slavic" - relating to the Slavs or their languages and culture.
Here, "славянские" is used as an adjective to describe "языки" (languages), indicating a specific category of languages.
Моя подруга изучает славянские языки.
My friend studies Slavic languages.
In this case, "славянском" is used as an adjective in the prepositional case to describe "районе" (district), specifying an area related to Slavic culture.
Этот музей изящных искусств расположен в славянском районе города.
This fine arts museum is located in the Slavic district of the city.
Here, "славянской" functions as an adjective in an instrumental case to qualify "культуры" (culture), indicating culture associated with the Slavic people.