In the 1960's a Professor called Neil Bartlett in the University of California Berkeley found that it is indeed possible to combine Xe with other elements. The first compound which he made was XePtF6 (xenon hexafluoroplatinate), which is rather complicated, but later, people have made simpler compounds like XeF6 (xenon hexafluoride).
The key idea is to combine Xe with a very ELECTRONEGATIVE element or species, that really like to grab electrons from other atoms. F (fluorine) is very electronegative. It also forms compounds with Kr (krypton) but these are less stable and more difficult to make.
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