Learn Danish: Apotekeren har mange smertestillende piller i skabet. - The pharmacist has many pain-relieving pills in the cabinet.

The base word for a pharmacy is et apotek, which becomes apoteket for "the pharmacy". The person who works there is en apoteker (a pharmacist). To say "the pharmacist", you add the standard -en ending, giving you apotekeren.

Because piller is plural, shouldn't smertestillende have a plural ending?

Usually adjectives change to match plural nouns, but smertestillende is a present participle (a verb form ending in -ende, similar to the English "-ing"). When these -ende words are used as adjectives, they never change their endings, regardless of whether the noun is singular, plural, or definite.

Smertestillende is a very long word. What are its root parts?

It is a compound made of two words: smerte meaning pain, and stillende meaning calming, quieting, or relieving. You will see this same -stillende ending in other medical contexts too, such as kløestillende (anti-itch).

Is the singular form of piller just pil?

No, the singular is en pille. When a Danish noun already ends in an unstressed -e, it usually forms its plural by just adding -r, which is why it becomes piller.