Can a multiclassed Hexblade warlock/monk use their Hex Warrior class feature on their Martial Arts unarmed strike?
How about the Pact of the Blade feature to make their unarmed strikes magical?
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Hex Warrior says:
...whenever you finish a long rest, you can touch one weapon that you are proficient with that lacks the two handed property.
Pact of the Blade says:
You can use your action to create a pact weapon in your empty hand. You can choose the form that this melee weapon takes each time you create it (see chapter 5 for weapon options).
Unarmed strikes are not weapons so they cannot be used. Not to mention that Pact of the Blade works by creating a weapon out of nothing or by transforming an existing magical weapon, neither of which can apply to unarmed strikes.
Unarmed strikes are not listed as a weapon in the PHB after the errata which says:
Unarmed strike doesn’t belong on the Weapons table.
Also, Jeremy Crawford has clarified here:
Unarmed strikes have always been weapon attacks. Here's where the confusion comes in: your unarmed strike (fist, elbow, knee, butt, etc.) is not considered by the rules to be a weapon the way a longsword is a weapon. But the rules let you make unarmed weapon attacks anyway.
The rule on unarmed strikes is an exception: they can be used for melee weapon attacks, despite not being weapons.
Of course, monk weapons will work as usual and both benefits could be applied to those.
The Hex Warrior class ability from Xanathar's Guide talks about weapons, and unarmed strike is not a weapon (it was, but was removed in errata and later reprints of the PHB), so this shows that the designers did not want weapon-specific features working with unarmed strike.
Similarly, Pact of the Blade talks about weapons as well. Of course, if you were planning to take 6 levels in monk, your unarmed strikes would be magical anyway as per the Ki-Empowered Strikes class feature.