Try to plot x^(2/3).. what happen for x<0 ?

08222019, 03:45 AM
(This post was last modified: 08222019 03:46 AM by josephec.)
Post: #1




Try to plot x^(2/3).. what happen for x<0 ?
Hi Friends
Why In HP PRIME is different (X^2)^(1/3) and (x^(1/3))^2 ? Pd. The first one plots for x<0 Thanks for Your answers. 

08222019, 06:45 AM
Post: #2




RE: Try to plot x^(2/3).. what happen for x<0 ?
I assume the Prime does simpy follow the basic rules of Mathematics:
In the first expression, we start with squaring x, which yields for all reals a positive result  thus the cubic root is defined everywhere. In the second expression, the cubic root is calculated first  but for reals is only defined for x >= 0. Thus the plot is left for x < 0. 

08222019, 08:08 AM
(This post was last modified: 08222019 08:10 AM by ijabbott.)
Post: #3




RE: Try to plot x^(2/3).. what happen for x<0 ?
You can redefine the second one as \( \big( \sqrt[3]{x}\big)^2 \) to square the real cube root of \( x\).
Note that \(x^\frac{1}{3}\) and \(\sqrt[3]{x}\) are treated differently, and that \(x^\frac{1}{3}\) usually produces a complex number when \( x < 0 \), and its square is also complex, so it cannot be plotted by the Function app. — Ian Abbott 

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