Exponents Issue

[Albert Chan]

(02-05-2020 10:42 PM)Claudio L. Wrote:  Wolfram Alpha seems to think it's a bad idea to simplify this too.

Mathematica "^" only simplify if c is integer:

• (a*b)^c → a^c * b^c
• (a^b)^c → a ^ (b*c)
  

To force above rules for other c, use PowerExpand, but result might not be correct.

x^(1/9)*(x*x^(1/3))^(1/6) // PowerExpand    → x^(1/3)

(02-05-2020 11:05 PM)CyberAngel Wrote:  Fractional or rational exponents using Power function differ from the Root function.

I tried XCas using root, but it made no difference.
From XCas help, it says root(a,b) returns b^(1/a) (root(2,3)=sqrt(3)).