I'm doing a little entry test (take home) for my College Algebra class, they make everyone do it to make sure you're up to speed for the course. With the help of the internet and brushing up on a few things, I've done fine, with one exception. One of the questions asks to simplify this expression: -27^-1/3 (-27 to the -1/3 power). I know that fractions in exponents equate to some radicals, as in this problem it could be converted to -27 in a negative cubed root, but can it be simplified more than that? If you plug it into a calculator, the answer comes to -1/3, but how do I get there?

According to Maple, it simplifies to -1/27*(-27)^(2/3)

I have no idea why though. Also it's apparently complex.

First thing is that you have to remember order of operations, so you do the - of the -27 LAST.

27 ^ 1/3 is 3 (cube root), so 27 ^ -1/3 is 1/3 (negative exponent is the reciprocal). Then throw the negative on there and get -1/3.

[...I might not have understood your question. You're trying to simplify, yes?]

-27[sup](-1/3)[/sup]

= (-1/27)[sup]1/3[/sup]

and since x[sup]1/n[/sup] is the same as the nth root of x

The above is equal to the cube root of -1/27 which is equal to -1/3

Thanks guys, that was what I was looking for. I forgot about the negative exponents and what they did.