Learn Hardcore German: Das Licht brennt hell im Treppenhaus. - The light burns brightly in the stairwell.

In German every noun is capitalized. Licht is a neuter noun (just like das Kind, das Haus), so it takes the definite article das in the nominative: das Licht.

What does brennt mean in this sentence?

Here brennt is the third-person singular present of brennen. It doesn’t mean “to burn” something (like fire destroying wood) but “to be lit” or “to shine.” So Das Licht brennt = “The light is on” or “The light shines.”

Why is hell not inflected (e.g. helles)?

Hell here is not an adjective modifying a noun but an adverb modifying the verb brennt. It answers “how?” (how is it shining?), so it stays in its base form: hell (brightly). If you wanted an adjective before a noun, you would inflect: ein helles Licht (a bright light).

What does im stand for in im Treppenhaus?

Im is the contracted form of in dem. When in (meaning “in/inside”) is used with a masculine or neuter definite article in dative case, you merge them:

in + dem Treppenhaus → im Treppenhaus

Why is Treppenhaus in the dative case?

The preposition in can govern accusative (motion into) or dative (location in). Here there is no motion; it describes location (“inside the stairwell”), so you use the dative. That’s why it’s dem Treppenhaus (contracted to im Treppenhaus).

Why is brennt in the third-person singular present tense?

The subject is das Licht (third person singular). In German present tense you conjugate brennen as follows:

ich brenne
du brennst
er/sie/es brennt
Hence Das Licht brennt = “The light is on / The light shines.”

Could I use leuchten instead of brennen?

Yes, leuchten also means “to shine” or “to give light,” but it often describes a stronger or more continuous glow (e.g. Der Mond leuchtet). Das Licht leuchtet hell im Treppenhaus is perfectly correct and maybe even a bit more vivid, but brennen is more idiomatic for lamps and bulbs.

Why is Treppenhaus written as one word?

German loves compound nouns. Treppenhaus combines Treppe (stair) + Haus (house/building) to mean “stairwell” or “staircase area.” In German you almost always write such compounds as one word.