Embarrassed to ask

[jebem]

(07-16-2014 06:01 AM)John R Wrote:  

(07-16-2014 02:08 AM)Waon Shinyoe Wrote:  (-8)^(2/3)=4

Careful -- fractional exponentiation of negative numbers is a thorny issue, and the answer is different depending on the assumed domain and the precise definition of the exponentiation operator (which was not specified here). Although 4 is typically the accepted answer in the real domain, a more general interpretation (based on analytic continuation of exponentiation in the complex domain) is that there are THREE answers of the form \[(-8)^{2/3}= \{4\omega, 4\omega^2, 4\},\] where \[\omega = -\frac{1}{2} + i\frac{\sqrt{3}}{2}\] is the so-called principal cube root of unity. (Try evaluating \(\omega^3\) if you don't believe it.) The first of these three answers, \[4\omega = -2 + i2\sqrt{3},\] would generally be considered the principal answer.

If you don't believe me, consult a higher authority: try evaluating (-8)^(2/3) on an HP-42S and see what it says.

Interesting... and my HP-15C gives me an Domain Error.
I mean, using -8^( 2/3)