Which of the following is the correct decreasing order of oxidizing power of perhalate ions?

The oxidizing power of perhalate ions depends on their standard reduction potentials. A higher positive standard reduction potential indicates a stronger oxidizing agent.

The standard reduction potentials ($E^{\circ}$) for the reduction of perhalate ions to halate ions in acidic medium are:
$E^{\circ}(\text{BrO}_4^- / \text{BrO}_3^-) = +1.74\text{ V}$
$E^{\circ}(\text{IO}_4^- / \text{IO}_3^-) = +1.65\text{ V}$
$E^{\circ}(\text{ClO}_4^- / \text{ClO}_3^-) = +1.20\text{ V}$

Since the reduction potential is highest for $\text{BrO}_4^-$ and lowest for $\text{ClO}_4^-$, the decreasing order of oxidizing power is $\text{BrO}_4^- > \text{IO}_4^- > \text{ClO}_4^-$.

The exceptionally high oxidizing power of $\text{BrO}_4^-$ is due to the relative instability of the $+7$ oxidation state of bromine, which arises from the poor shielding of the $3d$ electrons (d-block contraction or middle row anomaly).

Answer: $\text{BrO}_4^- > \text{IO}_4^- > \text{ClO}_4^-$