Help with rate constants in kinetics

Consider the rate constants below. Which
would correspond to the highest order reac-
tion?

1. k = 1.88 × 10−3 M−2· s−1
2. k = 8.79 × 102 M· s−1
3. k = 2.35 × 106 s−1
4. k = 4.46 × 10−1 M−1· s−1

I know the answer is 1. The key says it's a 3rd order reaction. I don't understand how to test each answer choice for the order. Could anybody please explain how to do so?

Thanks

for a reaction of order n reaction rate is given by :

rate = k X [A]^n


unit of rate is mole/L/s or M s^-1
unit of [A] is moles/L or M

1.unit of k is given as M^-2 s^-1

putting in rate expression..

M s^-1 = M^-2 s^-1 X M^n

M^3 = M^n

so n = 3 i.e. third order reaction

2.unit of k is given as M s^-1

putting in rate expression

M s^-1 = M s^-1 X M^n

M^n = 1

1 can be writtten as M^0

M^n = M^0

n = 0 i.e. zero order reaction

3.unit of k is given as s^-1

putting in rate expression..

M s^-1 = s^-1 X M^n

M = M^n

n = 1 i.e. first order reaction

4.unit of k is given as M^-1 s^-1

putting in rate expression...

M s^-1 = M^-1 s^-1 X M^n

M^2 = M^n

n = 2 i.e. second order reaction

so ans is 1.