The noun departure is a general term used to refer to an act or instance of going away or leaving (the time of departure; a hasty departure). It can also refer to a divergence or deviation, as from a standard or rule (a departure from accepted teaching methods). The noun exodus deals with the act of leaving on a larger scale, more specifically to a departure or emigration, usually of a large number of people: June marked the beginning of the annual summer exodus to the country and shore. When treated as a proper noun, Exodus refers to the departure of the Israelites from Egypt under Moses, or to the second book of the Bible, containing an account of the Exodus.
A person can laugh, that is, audibly express mirth or amusement, in many different ways. On the unrestrained side of the spectrum, one might guffaw, laughing loudly and boisterously. On the more subdued side, one might chuckle. The verb chuckle is defined as “to laugh softly or amusedly, usually with satisfaction.” It is also used to talk about laughing inwardly or to oneself—the way you might when reading (depending on the material!). To chuckle gleefully is to chortle, itself a portmanteau blending the words snort and chuckle.
The adjective powerful can refer to physical strength (a powerful athlete), great effectiveness (a powerful speech), or high potency (a powerful drug). But powerful overlaps with mighty only when describing people or entities that have great power, authority, or influence (a powerful nation). Mighty is chiefly used in a rhetorical manner to indicate uncommon or overwhelming strength or force (a mighty army). Though you might encounter it describing things of uncommon or overwhelming size (a mighty oak; a mighty river), or, things that are great in amount, extent, degree, or importance (a mighty accomplishment).