Consider the reactionA+2B⇌C whose rate at 25 ∘C was measured using three different sets of initial concentrations?

Rate = k [A]ᵃ [B]ᵇ

For trial 1 : 9.0 × 10⁻³ = k (0.50)ᵃ (0.030)ᵇ ..... [1]
For trial 2 : 1.8 × 10⁻² = k (0.50)ᵃ (0.060)ᵇ ..... [2]
For trial 3 : 3.6 × 10⁻² = k (1.00)ᵃ (0.030)ᵇ ..... [3]

[3]/[1]:
4 = 2ᵃ
2ᵃ = 2²
a = 2

[2]/[1]:
2 = 2ᵇ
2ᵇ = 2¹
b = 1

Put a = 2 and b = 1 into [1]:
9.0 × 10⁻³ = k (0.50)² (0.030)
k = 1.2

Hence, Rate = 1.2 [A]² [B]

When [A] = 0.50 M and [B] = 0.075 M :
Rate = 1.2 × (0.50)² × 0.075 = 2.25 × 10⁻² M/s