I'm having trouble simplifying this. ^3 to the square root of negative 27

Do you mean \sqrt{-27}^3 ?

You cannot solve it in the real numbers: \sqrt{-27}=3\sqrt{3}i , and \sqrt{-27}^3= -81\sqrt{3}i, where i:=\sqrt{-1} .

I wonder if the OP means this:


\sqrt[3] {-27}


What you're looking for is the cube root of -27, or a number N that satisfies N \times N \times N = -27 . Here's a hint: if N is a negative number the result is also negative: for example of N = -2 then (-2) \times (-2) \times (-2) = -8. Perhaps now you can come up with a value for N that works?

I think ebaines's guess makes more sense, but it is unusual to write "square root" in this case.