Here's why:

* Free radicals are atoms or molecules with an unpaired electron, making them highly reactive.

* BrO3- has a total of 26 valence electrons: 7 from bromine, 6 from each of the three oxygen atoms, and one extra electron due to the negative charge.

* These electrons are distributed in a way that all of them are paired, forming stable bonds within the molecule.

Therefore, there are no unpaired electrons in the BrO3- ion, and it does not possess any free radicals.