Final answer:
King Louis XIV had his nobles live lavishly at Versailles to keep them financially and politically weakened, unable to challenge his absolute rule, under the umbrella of reinforcing his power and control as encapsulated in 'Létat, c'est moi' - 'I am the state'.
Step-by-step explanation:
King Louis XIV encouraged the nobles of his court to live beyond their means as a strategic move to reinforce his absolute power. By having the nobility reside at the Palace of Versailles, engaged in opulent activities and vying for his favor, he assured that their finances (and thus their power) were depleted and consequently, they were less capable of funding rebellions against his rule. The nobles' preoccupation with displays of wealth and seeking the king's approval through extravagant living distracted them from plotting against him. This strategy of demanding they attend his court was a deliberate tactic to suppress any challenge to his authority, underpinning his famous notion 'Létat, c'est moi' ('I am the state'). Louis XIV's control over state affairs, coupled with France's mercantilist economy under his finance minister Jean-Baptiste Colbert, enabled the monarchy to prosper, although it greatly increased France's debt, setting the stage for future economic crises.