How are they different? Cube root vs the exponent of 1/3

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

Subscribe: https://www.youtube.com/user/MindYour...

Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas!

If you purchase through these links, I may be compensated for purchases made on Amazon. As an Amazon Associate I earn from qualifying purchases. This does not affect the price you pay.

If you purchase through these links, I may be compensated for purchases made on Amazon. As an Amazon Associate I earn from qualifying purchases. This does not affect the price you pay.

Book ratings are from January 2023.

My Books (worldwide links)
https://mindyourdecisions.com/blog/my...

My Books (US links)
Mind Your Decisions: Five Book Compilation
https://amzn.to/2pbJ4wR
A collection of 5 books:
"The Joy of Game Theory" rated 4.3/5 stars on 290 reviews
http://amzn.to/1uQvA20
"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" rated 4.1/5 stars on 33 reviews
http://amzn.to/1o3FaAg
"40 Paradoxes in Logic, Probability, and Game Theory" rated 4.2/5 stars on 54 reviews
http://amzn.to/1LOCI4U
"The Best Mental Math Tricks" rated 4.3/5 stars on 116 reviews
http://amzn.to/18maAdo
"Multiply Numbers By Drawing Lines" rated 4.4/5 stars on 37 reviews
http://amzn.to/XRm7M4

Mind Your Puzzles: Collection Of Volumes 1 To 3
https://amzn.to/2mMdrJr
A collection of 3 books:
"Math Puzzles Volume 1" rated 4.4/5 stars on 112 reviews
http://amzn.to/1GhUUSH
"Math Puzzles Volume 2" rated 4.2/5 stars on 33 reviews
http://amzn.to/1NKbyCs
"Math Puzzles Volume 3" rated 4.2/5 stars on 29 reviews
http://amzn.to/1NKbGlp

2017 Shorty Awards Nominee. Mind Your Decisions was nominated in the STEM category (Science, Technology, Engineering, and Math) along with eventual winner Bill Nye; finalists Adam Savage, Dr. Sandra Lee, Simone Giertz, Tim Peake, Unbox Therapy; and other nominees Elon Musk, Gizmoslip, Hope Jahren, Life Noggin, and Nerdwriter.

My Blog
https://mindyourdecisions.com/blog/

Twitter
  / preshtalwalkar  

Instagram
  / preshtalwalkar  

Merch
https://teespring.com/stores/mind-you...

Patreon
  / mindyourdecisions  

Press
https://mindyourdecisions.com/blog/press