Learn Finnish: Tämä on museon vanhin fossiili. - This is the oldest fossil in the museum.

When forming the superlative with the ending -in, a final -a or -ä on the base adjective drops out. Therefore, vanha loses its final -a before adding the marker, becoming vanhin.

The translation says 'in the museum', but the Finnish sentence uses the genitive museon. Why is that?

When expressing that something is the 'most [adjective]' within a specific place or group, Finnish typically uses the genitive case rather than a location case like the inessive (-ssa). You are literally saying 'This is the museum's oldest fossil.'

What is the stem for vanhin if I need to put it into a different case?

Superlatives ending in -in have a special stem when you add case endings: they change to -impa- or -imma- (due to consonant gradation). For example, if you wanted to say 'from the oldest fossil', it would be vanhimmasta fossiilista.