Introduction
In this problem, we are given a relation between pressure (p), length (z), temperature (theta), Boltzmann constant (k), and two unknown parameters a and b. We are required to determine the dimensional formula of a and b.

Step 1: Deriving the Dimensional Formula of p
From the given relation, we can write:
p = a/b * e^(-az/k*theta)

The dimensional formula of pressure is given by:
[P] = [M L^-1 T^-2]

Where, M represents mass, L represents length, and T represents time.

Step 2: Deriving the Dimensional Formula of e^(-az/k*theta)
Since e is a dimensionless quantity, we only need to determine the dimensional formula of (-az/k*theta).

From the given variables, we can write:
[-az/k*theta] = [L] * [K^-1] * [T]

Where, K represents temperature.

Step 3: Deriving the Dimensional Formula of a/b
From the given relation, we can also write:
a/b = p * e^(az/k*theta)

Therefore, the dimensional formula of a/b is:
[a/b] = [P] * [e^(az/k*theta)]

Step 4: Combining the Dimensional Formulae
Substituting the dimensional formulae of p, e^(-az/k*theta), and a/b in the given relation, we get:

[M L^-1 T^-2] = [P] = [P] * [e^(az/k*theta)] * [e^(-az/k*theta)]

Simplifying, we get:
1 = [e^(az/k*theta)] * [e^(-az/k*theta)]

Since the two terms in the above equation are dimensionless, we can equate their dimensional formulae as follows:

[1] = [e^(az/k*theta)] * [e^(-az/k*theta)]

Therefore, we get:

[L]^[K^-1] * [T] = [L]^[K^-1] * [T]

Step 5: Determining the Dimensional Formula of a and b
From the above equation, we can see that the dimensional formulae of a and b will cancel out, leaving us with:

[1] = [e^(az/k*theta)] * [e^(-az/k*theta)]

Therefore, the dimensional formula of a/b is:

[a/b] = [e^(-az/k*theta)]

And the dimensional formula of a is:

[a] = [P] * [e^(-az/k*theta)]

And the dimensional formula of b is:

[b] = [e^(az/k*theta)]

Conclusion
In this problem, we used the given relation between pressure, length, temperature, Boltzmann constant, and two unknown parameters a and b to determine their dimensional formulae. We found that the dimensional formula of a is [P] * [e^(-az/k*theta)], and the dimensional formula of b is [e^(az/k*theta)].