Spray Instant Pot insert with cooking spray. Place chicken in Instant Pot. Season with salt, garlic powder and pepper on all sides.
In a medium bowl, whisk together barbecue sauce, root beer, Worcestershire sauce and ¼ cup water. Pour sauce over the chicken (do NOT stir – you want the sauce on top of the chicken to prevent scorching on the bottom).
Seal the release valve, place the lid on the Instant Pot, and turn to lock the lid.
Press the “Manual” button on high pressure, and then set the timer to 10 minutes.
It will take about 10 minutes for the pot to heat up and build up pressure, then the chicken will cook for an additional 10 minutes. Once the 10-minute timer is done, quick release the pressure from the pot, sliding the steam release handle to the “Venting” position, releasing all of the steam until the float valve drops down.
Open the lid and press the “cancel” button.
Remove the chicken and allow to rest on a cutting board for 5-10 minutes before slicing or shredding. Return shredded chicken to the pot, toss with sauce, and serve.