The phrase "assert their power" is correct and usable in written English.
It can be used in contexts where individuals or groups are demonstrating or claiming authority or control over a situation or others.
Example: "In times of crisis, some leaders may choose to assert their power to maintain order and stability."
Alternatives: "exert their influence" or "demonstrate their authority."
Yet, as this exhibit shows, women have also used underwear to assert their power and status.
What were they trying to say? Was it a new body language trick to assert their power?
Money men assert their power, scripts get rewritten, egos have to be massaged and last-minute crises intervene.
Others say women use language to assert their power in a culture that, at least in days gone by, asked them to be sedate and decorous.
There is blossoming love between Otelo and New Year's sister, Dezi (Nolwazi Shange), but there are also rumblings in the outside world as rival factions in the great events that are transforming the country assert their power.
The deaths and injuries of thousands of garment workers in Bangladesh raise the question of how American and European consumers might assert their power to change appalling factory conditions half a world away.
With powerful leading women like Sansa, Yara, and Dany firmly asserting their power in season six's penultimate episode, and a group of secondary women pushing forward, too, the women of Game of Thrones are taking the reins and learning to reign.
In England, both houses of Parliament have asserted their power to punish contumacious acts.
A cadre of the don's underlings, including his son, stepped into the vacuum and asserted their power.
In both the maritime and engineering industries, employers had asserted their power by combining in national federations.
Just as cyberbullies use electronic devices to hurt others, food allergy bullies "are asserting their power using the allergen," Dr. Shetgiri said.
