Please help me calculate the following:
16^(-1/2)
(27)^(1/3) - with questions that have two brackets, only the first number has brackets on paper.
(27)^(-1/3)
(-27)^(1/3)
(-27)^(-1/3)
(-2)^(-3)
Well, if you try to take the square root (or any even root) of a negative number, you will not get a real answer (because the square of any real number is nonnegative). However, you can take cube roots of a negative number, and in fact you can take the $\displaystyle n^{\rm th}$ root of a negative number as long as $\displaystyle n$ is odd.
Thus, $\displaystyle \sqrt[3]{-27} = -3$, for example, because $\displaystyle (-3)^3 = (-3)(-3)(-3) = -27$.