The data in the table below were obtained for the reaction: a + b → p experiment number [a] (m) [b] (m) initial rate (m/s) 1 0.273 0.763 2.83 2 0.273 1.526 2.83 3 0.819 0.763 25.47 the magnitude of the rate constant is

If we tabulate the data given, we obtain the following table;
Exp            [a](m)            [b] (m)         Initial rate (m/s)
1                 0.273          0.763           2.83
2                 0.273          1.526           2.83 
3                 0.819           0.763         25.47 
the rate equation 
rate = k [a]ˣ[b]ⁿ
where k = rate constant 
x and n are order of reaction with respect to a and b respectively
lets take experiment 1 and 2 where [a] is constant so we can find the order of reaction with respect to b

2.83 m/s = k[0.273 m]ˣ[0.763 m]ⁿ ---> 1)

2.83 m/s = k [0.273 m]ˣ[1.526 m]ⁿ > 2)
2)/1)
1 = [1.526/0.763]ⁿ
1 = 2ⁿ
n = 0
next we have to find out x, we have to take experiment 1 and 3 where [b] remains constant 
25.47 m/s =k [0.819]ˣ[0.763]ⁿ --3)
2.83 m/s = k[0.273 m]ˣ[0.763 m]ⁿ ---> 1)

3)/1)
25.47/2.83 = [0.819/0.273 m]ˣ
9 = 3ˣ
x = 2
therefore order with respect to a = 2 and order with respect to b = 0
rate = k[a]²[b]⁰
to find k lets substitute 1st experiment values 
2.83 m/s = k [0.273 m]² [0.763]⁰
k = 2.83/0.0745
k = 37.98 m⁻¹s⁻¹