Explanation:
The oxidation state of an element is the charge it would have if all its bonds were ionic.

Br3O8:
Br3O8 is a compound containing three bromine atoms and eight oxygen atoms.

Br:
Bromine is a halogen that usually has an oxidation state of -1 when it forms compounds.

O:
Oxygen usually has an oxidation state of -2 when it forms compounds.

Calculation:
The sum of the oxidation states of all the atoms in a compound must equal the charge on the compound.

Charge on the compound:
The compound is neutral, so the charge on the compound is zero.

Oxidation state of oxygen:
There are eight oxygen atoms in the compound, so the total charge contributed by them is -16.

Oxidation state of bromine:
Let the oxidation state of bromine be x.
The total charge contributed by the three bromine atoms is 3x.

Equation:
Total charge contributed by all atoms = Charge on the compound
3x + (-16) = 0
3x = 16
x = 16/3

Answer:
The oxidation state of the central bromine atom in Br3O8 is +16/3.