Given Information:
- Set A contains 'a' elements.
- Set B contains 'b' elements.

Objective:
To find the values of 'a' and 'b' such that the power set of A contains 16 more elements than the power set of B.

Solution:
Let's break down the problem into smaller steps.

Step 1: Understanding the Power Set
The power set of a set is the set of all possible subsets of that set, including the empty set and the set itself. For example, the power set of {1, 2} is {{}, {1}, {2}, {1, 2}}.

Step 2: Calculating the Size of Power Sets
The size of the power set is given by 2^n, where n is the number of elements in the original set. This formula holds true because for each element in the original set, there are two possibilities: either it is included in a subset or it is not.

Step 3: Formulating the Equation
Let's denote the number of elements in set A as 'a' and the number of elements in set B as 'b'. Therefore, the sizes of their power sets will be 2^a and 2^b, respectively.

According to the given information, the power set of A contains 16 more elements than the power set of B. Mathematically, we can represent this as:

2^a = 2^b + 16

Step 4: Solving the Equation
To find the values of 'a' and 'b', we need to solve the equation we formulated in the previous step.

Taking the logarithm (base 2) of both sides of the equation, we get:

log2(2^a) = log2(2^b + 16)

Using the logarithmic property log2(x^y) = y * log2(x), we simplify the equation further:

a = b + 16 / log2(2)

Since log2(2) = 1, the equation becomes:

a = b + 16

Therefore, the values of 'a' and 'b' that satisfy the given condition are 'b' and 'b + 16' respectively.

Conclusion:
The value of 'b' is given by 'b', and the value of 'a' is given by 'b + 16'.