WolframAlpha gives different results if you try the cube root of -1 versus taking -1 to the exponent 1/3. Why is this happening? There is a good reason for the difference, which involves complex numbers and roots of equations. Special thanks this month to: Kyle, Lee Redden, Mike Robertson, Daniel Lewis. Thanks to all supporters on Patreon!   / mindyourdecisions  

References
https://www.wolframalpha.com/input?i=...
https://www.wolframalpha.com/input?i=...
https://www.wolframalpha.com/input?i=...
https://en.wikipedia.org/wiki/Square_...
https://en.wikipedia.org/wiki/Functio...)
https://en.wikipedia.org/wiki/Princip...
https://en.wikipedia.org/wiki/Princip...
https://en.wikipedia.org/wiki/Nth_root
https://math.stackexchange.com/questi...
https://blog.wolframalpha.com/2013/04...
Complex Variables and Applications, James Ward Brown, Ruel V. Churchill, 7th edition, Chapter 1 Section 8, Roots of Complex Numbers

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