To calculate this expression, we need to follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).

First, let's calculate 15.5^30:
15.5^30 ≈ 1.036^30 ≈ 2.166

Now, we can substitute this value back into the original expression:
4^15.5^30 = 4^2.166 ≈ 18.38

Therefore, 4^15.5^30 is approximately equal to 18.38.