**Advice: **
Fractional powers of negative numbers

Maple's mathematics is largely based on complex numbers rather than real numbers. In particular, it uses the "principal branch" of fractional powers: the principal branch of
has argument between
and
, and the argument of
is
.

So for example:

`> `
**evalc((-1)^(1/5));**

`> `
**evalf(%);**

`> `
**evalf(argument(%)/Pi);**

The
**surd**
function provides "elementary"
'th roots, i.e. if
is a negative number and
is odd, then
**surd(x,n)**
is the real (negative)
'th root of
.

`> `
**surd(-8,3);**

In order to have a somewhat nicer syntax, as well as covering rational exponents with numerators other than 1, I have defined an infix-form operator
**&^**
. This is part of the Maple Advisor Database, and must be read in before being used:

`> `
**readlib(`&^`);**

`> `
**(-1)&^(2/5), (-1) &^ (3/5);**

For positive , is the same as . For negative , if is a fraction we have the following cases:

`> `
**assume(x<0); **

and both odd:

`> `
**x &^ (3/5);**

even, odd:

`> `
**x &^ (4/5);**

odd, even: is complex.

`> `
**x &^ (3/8);**

When is not known to be real, and is a fraction, is written as a surd. When p is given in decimal form, it is converted to a fraction.

`> `
**x:= 'x': x &^ (3/8);**

`> `
**x &^ 0.375;**

`> `
**plot(x &^ (2/3), x = -1 .. 1);**

`> `
**plot(x &^ (3/5), x = -1 .. 1);**

**See also:**
__^__
,
&^
,
__surd__

**Maple Advisor Database **
R. Israel, 1998