Answer
See the work below
Work Step by Step
We can determine order of a reaction by adding the powers of concentration term in the rate law expression,
1) $Rate = k[NO_2]^2 $
order of the reaction = 2
2) $Rate = k$
order of the reaction = 0
3) $Rate = k[H_2][Br_2]^{\frac{1}{2}}$
order of the reaction = 1+$\frac{1}{2}$ = $\frac{3}{2}$
4) $Rate = [NO]^2[O_2]$
order of the reaction = 2+1 = 3
