# silly? - math - question about fractional powers of negative base

hello @all,

there are some questions and bugs around about the evaluation of fractional powers (roots) from negative bases, e.g. -8^(1/3) is the third root from -8 and thus -2, while -8^(1/2) results in an imaginary number 'i * squareroot(8)' [math: i=squareroot(-1)], and is not representable in spreadsheets ...

a simple marginal question of these problems: fractions can be 'extended', so (-1)^(1/3) would / should be the same as (-1)^(2/6)?

but if you now evaluate this according to school maths (base powered to a fraction is 'denominator root' from 'base to power of numerator'):

you get once ((-1)^1)^(1/3) - or cube root of '-1' - so '-1',

and once ((-1)^2)^(1/6) - or 6th root of '-1 squared', thus 6th root of 1, thus 1,

that can't be true for both?

probably there are some rules or definition restrictions or additional solutions in 'math'? but i don't remember if we were told this in school, and i couldn't find instant answer on the web, i hope someone here knows about ...

or do I have a cardinal error in thinking somewhere?

(why am i asking this question here ... imho calc should try to produce mathematical correct results, and for that such questions are important)

tia fah,

b.

Please remove tag

`math`

because it advertises issues with the formula editor. Instead use the unabbreviated`mathematics`

.@ajlittoz: thanks, i'd try to 'retag' math by mathematics, found editing the headline, the question, but nothing for the tags :-(

Retagging is a bit whimsical. When you have entered/replaced a tag, you must hit

`Enter`

twice.