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?

Oops, yeah, I forgot the parenthesis when checking in a calculator — Tyler, May 14 '15 at 00:31

score 0 · Answer 1 · answered May 14 '15 at 00:33

0

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

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

So positive 1.

answered May 14 '15 at 00:33

score 0 · Answer 2 · answered May 14 '15 at 02:42

0

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

answered May 14 '15 at 02:42

Valentin

2 Answers2