'exhibiting themselves' is a correct and usable phrase in written English.
It is typically used to describe when people or animals show off or display their abilities or behaviors in order to draw attention or gain approval. For example, "The children were exhibiting themselves in front of the judges, trying to show off their dance moves."
The dancers seemed not to believe in them, merely to be ravenously exhibiting themselves in them.
I was delighted to find that Rego's knowing, busy, cruel little girls were not being viewed through a keyhole in a version of what the butler saw, but were exhibiting themselves to a public for which they had scant regard.
For the gala Dec. 14 party to open a new Prada store in SoHo, New Yorkers pulled out all the sartorial stops, exhibiting themselves in slip dresses, crocodile pumps, ermine tippets, Brioni suits, big diamonds and all the other delirious markers of high style.
Gender and racial inequality continue to exhibit themselves in new ways.
It's not in the normal course of events that those behaviors exhibit themselves.
A dozen princesses exhibit themselves in vain (wittily snapped against a wall, their shifty eyes tell all).
Before the panel of 6 artists, art historians and writers began their discussion, 3 well-known body builders exhibited themselves.
In the razor-sharp recital culture, which requires artists to exhibit themselves vulnerable and naked onstage, Mr. Bostridge takes the vulnerability to an extreme.
"Several artists used their own bodies as their medium," she says, "including Gilbert and George, who exhibited themselves as living sculpture, and Hannah Wilke, who posed nude to mimic a controversial Duchamp sculpture".
Though he's at pains to point out how much his mother also cared for him, her fearfulness and self-pity were her greatest weapons and exhibited themselves in extraordinary declarations and actions.
He was also involved with an avant-garde group, the Neo-Naturists (started by his then girlfriend, Jennifer Binnie), who would paint their bodies and exhibit themselves at nightclubs and galleries.
