Learn Hardcore Korean: janggeori unjeoneun pigonhaeyo.

장거리 운전 is a noun phrase made of 장거리 (long-distance) + 운전 (driving). In Sino-Korean, 장(長) means long and 거리 means distance, so 장거리 = long-distance. 운전 comes from the verb 운전하다 (to drive), here used as the noun “driving.”

Why is 은 attached to 운전, and what role does it play?

은 is the topic particle. It marks 장거리 운전 as the topic of the sentence, signaling that what follows (“is tiring”) is a general comment about long-distance driving.

Is 피곤해요 an adjective or a verb? How does it fit into Korean grammar?

Korean descriptive verbs like 피곤하다 are often called adjectives in English, but grammatically they behave exactly like verbs (형용사). They conjugate just like action verbs. 피곤해요 is the polite present form meaning “is tired” or “feels tiring.”

Why is the dictionary form 피곤하다, and how do you conjugate it?

피곤하다 is formed by the Sino-Korean noun 피곤 (fatigue) + 하다 (to do). To make it polite present, drop -다 and add -해요:
피곤하다 → 피곤해요 (“is tired”).

How do you say the same sentence in informal (반말) and formal (합쇼체) styles?