Given that log base a of b equals 17, we can rewrite it as:

loga(b) = 17

Since Loga^4√(a\b) is equivalent to 4*loga(√(a\b)), we can rewrite it as:

4*loga(√(a\b))

Now, let's simplify the expression √(a\b) first:

√(a\b) = (a/b)^(1/2) = a^(1/2) / b^(1/2) = √a / √b

So, our expression becomes:

4loga(√(a\b)) = 4loga(√a / √b)

Now, we know that loga(b) = 17, so loga(a^n) = n. Therefore:

4loga(√a / √b) = 4(1/2)loga(a) - 4(1/2)*loga(b)

= 2 - 4(1/2)17

= 2 - 34

= -32

Therefore, Loga^4√(a\b) = -32.