Unchecked Power used on my Glask Mixologist. Can I play the unit to the Battle Glask was on?

Yes, you can play the unit to the battlefield where Glasc Mixologist died.

According to the rules for battlefield control and Deathknell timing, here is how the sequence of events unfolds:

The Ruling

Because Unchecked Power is a spell, it creates a chain. When Unchecked Power kills your Glasc Mixologist, its Deathknell trigger is placed on the chain as a pending item before the unit is moved to the trash. Per the Unleashed rules update regarding Rule 187.4.c, you do not lose control of a battlefield while there are items on the chain.

Since you control the battlefield where Glasc Mixologist died, and because the presence of the Deathknell ability on the chain prevents you from losing control, you have the necessary permission to play the unit to that specific battlefield.

Sequence of Events

1. Resolution: You resolve Unchecked Power. Glasc Mixologist is destroyed.
2. Deathknell Trigger: Glasc Mixologist's Deathknell ability triggers and is added to the chain as a pending item.
3. No Loss of Control: Even though Glasc Mixologist is gone, you do not lose control of the battlefield because an item (the Deathknell trigger) is still on the chain.
4. Chain Resolution: You resolve the Deathknell trigger. You play your chosen unit from your trash to the battlefield where Glasc Mixologist died.
5. Finalization: The chain clears, and you successfully maintain control of the battlefield because a unit is present when the cleanup completes.

This interpretation is based on the interaction between Rule 187.4.c and the Deathknell ability as clarified in the Unleashed rules update.