Sign of fractional exponent

Question

What is the sign of $-1^{\frac{2}{3}}$? I thought it was positive 1 because it involves squaring, but that doesn't seem to be the case. Why?

Answer 1

If you rewrite it, it becomes $\sqrt[3]{(-1)^2}$.

$(-1)^2 = 1$ and $\sqrt[3]{1} = 1$

So positive 1.

Answer 2

$x^y$ is not defined for negative $x$ and real $y$. Otherwise, we would have $(-1)^{1/3} = -1$, but $(-1)^{2/6}=1$.