If a die is considered an exploding die, you may re-roll it whenever you get a six, and add the original roll and the additional roll to the total result. You may re-roll the dice as many times as you can continue to roll a six.
Example
You have an exploding die and you roll a 6. You re-roll and get a 6. You re-roll again and get a 5. The chain ends because you did not roll a 6 on the third roll. The total value of this die is 17.