Does $\sqrt {-9} = -(9^{1/2})\;?$

Question

The reason I’m asking this question is I know for a fact that the fraction on the power is somewhat the same as root degree…

But I also know as a fact that you cannot calculate the root of a negative number.

So my question basically is : Does $\,-9^{1/2}$ = $\sqrt{-9}\;?$

Since I believe $-9^{1/2}= -3$ (according to my calculator)

but, when I try $\sqrt{-9}$, it’s undefined

so which one is the correct answer ?

Thanks in advance

Answer 1

Depends on the parentheses

$-(9)^{1/2}$ implies negative of the square root of nine, which is $-3$

$(-9)^{1/2}$ implies square root of negative nine, which is not a real number.

Entering $-9^{1/2}$ would be interpreted as $-(9)^{1/2}$ by the calculator (which is equal to $-3$).