How do you simplify #(1/2) ^ (5/2) #?
When you have an exponent that is a fraction, in this case, 5/2, the numerator becomes the exponent of the original value (1/2), and the denominator becomes the index of a radical (the expression above the radical symbol)
Obviously those are confusing terms that don't really mean anything; an easy way to remember it is that the numerator moves down, and the denominator moves to the side:
In this case, the index is 2. When the index is 2, the expression is just "the square root of," so you don't need to write the index if and only if it's 2, but it's there for clarity.
To simplify it even further, we can evaluate:
Now we are left with
To simplify this even further, you would have to simplify
Don't forget that 1 is a perfect square! Now we have:
Unfortunately, we can't leave radicals in the denominator, so we have to multiply the top and bottom by