It depends. If the parent is the custodial guardian, and they qualify to claim the dependents, then they would enter them on their tax return regardless of who has the POAs. If you are asking if you could claim them as a dependent, please review the rules in the link below to see if they would be qualifying relatives for you. If they do qualify, then you may receive the Other Dependent Credit (ODC).
To determine if a person is a qualifying dependent or qualifying relative for a taxpayer review the link below.
If the persons for whom you have the POAs are adults without a parent or other person allowed to claim them, then they would file their own tax return. In this case they would not be entitled to the Child Tax Credit (CTC) or Other Dependent Credit (ODC). Likewise they would not be entitled to the Advance Child Tax Credit (ACTC).
Please update with additional details, including the state if this is a state tax question.
**Say "Thanks" by clicking the thumb icon in a post
**Mark the post that answers your question by clicking on "Mark as Best Answer"