Chainsaw-equipped or chainsaw equipped?

Hyphens are used to connect words when it's unclear which words are modifying which other words. Connecting the two words that modify each other with a hyphen can make a big difference in the meaning of a sentence.

Compare these different ways of using a hyphen with the same words: A "big-time traveller" is someone who travels a lot. A "big time-traveller" is a large person who can move through time. Very different meanings! Without the hyphen, "big time traveller" could have either meaning.

A similar example is "a man-eating cow". With the hyphen the phrase describes a cow that eats people. Without the hyphen, it describes merely a man eating cow meat: "a man eating cow". (Note that "a man eating-cow" would not be correct, because hyphens and verbs work differently: "a man cow-eating" is technically correct but sounds strange.)

The most common way you will see hyphens used is to combine two words into a single adjective. Examples are "English-speaking Russian", "chainsaw-equipped truck", "beer-loving vegetarian", "man-eating bear".