Question

Can someone please explain why (-9)1/2 is not a real number but -9 1/2 is a real number

Answer 1

This only makes sense if you meant

√(-9) vs - (√9)

remember we cannot take the square root of a negative number, that would be an imaginary or complex answer.
but by the order of operation for -√9
we take the square root first, and then make the answer negative, so
- √9 = -3

Answer 2

So are you saying that (-9)1/2 and
-9 1/2 is not a real number because that is how the problem was written

Answer 3

I assumed that you meant

(-9)^(1/2)
which is the same as √-9 , which of course is not real

vs

-(9^(1/2))
which is -√9
which is -3

the ^ is the generally accepted symbol to indicate an exponent,
e.g. x^2 is x squared, x^5 is x to the fifth, etc