a) 5^√32 + 3^√-8

First, let's simplify the expressions inside the radicals:
√32 = √(16 2) = √16 √2 = 4√2
√-8 = √(-1 * 8) = i√8 = 2i√2

Now, substitute these values back into the original expression:
5^4√2 + 3^2i√2

This expression is already in its simplest form.

b) 124^√1 - 63^√0.125

Let's simplify the expressions inside the radicals first:
√1 = 1
√0.125 = √(1/8) = 1/(√8) = 1/(2√2) = √2/4

Now, substitute these values back into the original expression:
124^1 - 63^(√2/4)

This expression is already in its simplest form.