To “take a powder” means to leave quickly, to sneak out.
Christine Ammer’s The Facts on File Dictionary of Clichés (2006) says, “To leave quickly. The origin of the expression is obscure, even though it is relatively recent (twentieth century). Since about 1600 “a powder” has meant “a hurry,” possibly derived from the speed of gunpowder. This meaning persisted well into the 1800s, mainly in Britain. In the 1920s, however, in popular literature, characters departing in haste were said to take a “runout powder.” P.G. Wodehouse used it in Money in the Bank (1942). One writer has suggested this might refer to a laxative, but that interpretation seems unlikely. Moreover, the French have a similar expression, Prendre la poudre d’escampette: ‘To take the scampering powder,’ or, in more idiomatic terms, ‘to bolt.'”
This was a popular expression in the US by 1925, part of gangster slang and old-time hard-boiled fiction and meant to depart or escape, often to avoid a difficult situation. “Scram”was a popular synonym.
“Take a powder” was a common phrase as a doctor’s instruction, most commonly referring to headache remedies or purgatives, which came in the form of small envelopes of powder to be mixed with water. But “take a powder” in the sense of consuming a medicinal powder goes back a long way. Between 1600 and 1900, “take a powder” seems to have been understood to refer almost exclusively to medicinal powders.
The “disappear” sense of “take a powder” almost certainly arose as a shortening of the expression “take a runout powder,” which appears in Google Books matches as early as 1914 (in a novel that used quite bit of US hobo slang), and which became widespread in other subgenres of US slang by the early 1920s.
The phrase first appeared in the Washington Post in 1916 in, “Look at the two birds trying to take a ‘run-out’ powder on the eats.” People trying to leave a restaurant without paying the bill still happens.
I occasionally hear someone say, “I’m gonna take a powder,” but now it means simply, “I’m outta here!” And I am — I have no more to say about powder.