A tooth sharpener is a device used by the Ferengi to keep their teeth as sharp as possible.
Famed Ferengi explorer Milch the Wanderer was said to have purchased the planet Wohoken for a crate of tooth sharpeners. (DS9 reference: Legends of the Ferengi)
When Quark and Rom were children, Rom used a latinum tooth sharpener, while Quark had to use a wooden chewstick. (DS9 episode: "Family Business")
In 2372, Nog sold Worf his tooth sharpener before he left Deep Space 9 for Starfleet Academy. (DS9 episode: "Little Green Men")
Later that year, a Dopterian burgled Worf's quarters, stealing several items, including his tooth sharpener. (DS9 episode: "Bar Association")
In 2376, holographic advertisements for tooth sharpeners were being shown in the Fram Memorial Spaceport when Quark, Nog and Ro Laren arrived there. (DS9 novel: Ferenginar: Satisfaction is Not Guaranteed)