values of a $\displaystyle\lim_{x \to -\infty} x^a$ For which values of $a$ the following limit is true?
$$x,a\in \mathbb R$$
$$\displaystyle\lim_{x \to -\infty} x^a = -\infty$$
For whole even numbers that would be false,
and for whole odd numbers, that would be true.
What about the rest?

Real exponents with negative bases is actually not well-defined. You can read this short explanation:
http://en.wikipedia.org/wiki/Exponentiation#Real_exponents_with_negative_bases
