(the square root of)32a(to the 5th power)b(to the 8th power)?

Answer 1

First, use the notation sqrt [(32a)^5 b^8]
I suppose you want to simplify this (get as much junk as you can outside the sqrt. You can take out (32a)^4 and b^8. When you do so, simply divide the exponents by 2. Then
32a^2b^4 sqrt (32a)
Still more you can do. Since 32=16x2, the 16 (or 4^2) can also come out. Then we have
128 a^2 b^4 sqrt (2a)

Answer 2

Im assuming you mean this:

sqrt(32a^5 * b^8)

a^2*b^4*sqrt(16*2a)

4*a^2*b^4*sqrt(2a)