It's (x+1/4)^3/2, so when you take the 1/4 out of the brackets it becomes (1/4)^3/2 = (1/2)^3 = 1/8.
As I was checking my answers in my solution manual, one of the parts in it was this:
How do I change from x + 1/4 from the first part, into [1/8 (4x+1) ...] from the second part? I thought the x + 1/4 would turn into 1/4(4x + 1)?
Where did the 1/8 come from?