{VERSION 2 3 "IBM INTEL NT" "2.3" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 
0 }{CSTYLE "Hyperlink" -1 17 "" 0 1 0 128 128 1 0 0 1 0 0 0 0 0 0 }
{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "2
D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 0 21 "" 
0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 }{CSTYLE "Help Heading" -1 26 "" 1 14 0 
0 0 0 0 1 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }
{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 
0 0 0 0 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 
{CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 
0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Bulle
t Item" 0 15 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 
0 -1 3 3 0 0 0 0 0 0 15 2 }}
{SECT 0 {SECT 0 {PARA 0 "" 0 "" {TEXT 26 10 "Function: " }{TEXT -1 35 
"&^ - \"elementary\" fractional powers" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT 26 18 "Calling sequence: " }}{PARA 0 "" 0 "
" {MPLTEXT 0 21 7 "x &^ p;" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 
"" 0 "" {TEXT -1 11 "Parameters:" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 4 "x
, p" }{TEXT -1 51 " - any algebraic expressions.  Numerical values of \+
" }{MPLTEXT 0 21 1 "p" }{TEXT -1 28 " should be rational numbers." }}}
{SECT 0 {PARA 0 "" 0 "" {TEXT 26 12 "Description:" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 15 "" 0 "" {TEXT -1 154 "Maple's mathematics is \+
largely based on complex numbers rather than real numbers.  It uses th
e \"principal branch\" of fractional powers. In particular, if " }
{XPPEDIT 18 0 "z" "I\"zG6\"" }{TEXT -1 31 " is a negative real number \+
and " }{XPPEDIT 18 0 "p" "I\"pG6\"" }{TEXT -1 29 " is real but not an \+
integer, " }{XPPEDIT 18 0 "z^p" ")%\"zG%\"pG" }{TEXT -1 184 " is not r
eal.  That is not the branch that is generally used in more elementary
 mathematics, where, for example, the cube root of a negative number w
ould be taken to be negative.  The " }{MPLTEXT 0 21 4 "surd" }{TEXT 
-1 173 " function can be used to obtain these \"elementary\" roots, bu
t it is comparatively clumsy notation and does not cover fractional ex
ponents with numerators other than 1.  The " }{MPLTEXT 0 21 2 "&^" }
{TEXT -1 52 " operator is intended to address these shortcomings." }}
{PARA 15 "" 0 "" {XPPEDIT 18 0 "x &^ p" "-%#&^G6$%\"xG%\"pG" }{TEXT 
-1 23 " is always a branch of " }{XPPEDIT 18 0 "x^p" ")%\"xG%\"pG" }
{TEXT -1 1 "." }}{PARA 15 "" 0 "" {TEXT -1 13 "For positive " }
{XPPEDIT 18 0 "x" "I\"xG6\"" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "x &^ p" 
"-%#&^G6$%\"xG%\"pG" }{TEXT -1 16 " is the same as " }{XPPEDIT 18 0 "x
^p" ")%\"xG%\"pG" }{TEXT -1 16 ".  For negative " }{XPPEDIT 18 0 "x" "
I\"xG6\"" }{TEXT -1 5 ", if " }{XPPEDIT 18 0 "p =m/n" "/%\"pG*&%\"mG\"
\"\"%\"nG!\"\"" }{TEXT -1 44 " is a fraction we have the following cas
es: " }}{PARA 15 "" 0 "" {TEXT -1 3 "-  " }{XPPEDIT 18 0 "m" "I\"mG6\"
" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "n" "I\"nG6\"" }{TEXT -1 11 " bot
h odd: " }{XPPEDIT 18 0 "`&^`(x,(m/n)) = -(-x)^(m/n);" "/-%#&^G6$%\"xG
*&%\"mG\"\"\"%\"nG!\"\",$),$F&F+*&F(F)F*F+F+" }}{PARA 15 "" 0 "" 
{TEXT -1 2 "- " }{XPPEDIT 18 0 "m" "I\"mG6\"" }{TEXT -1 7 " even, " }
{XPPEDIT 18 0 "n" "I\"nG6\"" }{TEXT -1 6 " odd: " }{XPPEDIT 18 0 "`&^`
(x,m/n) = (-x)^(m/n);" "/-%#&^G6$%\"xG*&%\"mG\"\"\"%\"nG!\"\"),$F&F+*&
F(F)F*F+" }}{PARA 15 "" 0 "" {TEXT -1 2 "- " }{XPPEDIT 18 0 "m" "I\"mG
6\"" }{TEXT -1 6 " odd, " }{XPPEDIT 18 0 "n" "I\"nG6\"" }{TEXT -1 7 " \+
even: " }{XPPEDIT 18 0 "`&^`(x,(m/n));" "-%#&^G6$%\"xG*&%\"mG\"\"\"%\"
nG!\"\"" }{TEXT -1 12 " is complex." }}{PARA 15 "" 0 "" {TEXT -1 5 "Wh
en " }{XPPEDIT 18 0 "x" "I\"xG6\"" }{TEXT -1 30 " is not known to be r
eal, and " }{XPPEDIT 18 0 "p" "I\"pG6\"" }{TEXT -1 16 " is a fraction,
 " }{XPPEDIT 18 0 "x&^p" "-%#&^G6$%\"xG%\"pG" }{TEXT -1 24 " is writte
n as a surd.  " }}{PARA 15 "" 0 "" {TEXT -1 5 "When " }{XPPEDIT 18 0 "
p" "I\"pG6\"" }{TEXT -1 57 " is given in decimal form, it is converted
 to a fraction." }}{PARA 15 "" 0 "" {TEXT -1 89 "This operator is part
 of the Maple Advisor Database, and must be read in before use with " 
}{MPLTEXT 0 21 14 "readlib(`&^`);" }{TEXT -1 24 " (note the back quote
s)." }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 26 9 "Examples:" }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 14 "readlib(`&^`);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#:6$%\"xG%\"pG6$%\"nG%\"dG6$%XMaple~Advisor~Database~1.0
0~for~Maple~V~Release~4~and~5G%gnCopyright~(c)~1998~by~Robert~B.~Israe
l.~~All~rights~reservedG6\"@)5-%%typeG6$9%%(integerG-%#isG6#1\"\"!9$)F
:F3-F16$F3%&floatG-%#&^G6$F:-%(convertG6$F3%)rationalG-F1FDC%>8$-%&num
erG6#F3>8%-%&denomGFL@%-F66$F:%%realG@'-F16$FI%%evenG)-%$absG6#F:F3-F1
6$FN%$oddG*&-%'signumGFfn\"\"\"FYF]o*&-%%surdG6$F[oFNF]oFYF]o-F`o6$)F:
FIFN.-F@6$F:F3F-F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "evalc
((-1)^(1/3)), surd(-1,3), (-1)&^(1/3);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6%,&#\"\"\"\"\"#F%*&%\"IGF%\"\"$F$F$!\"\"F*" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 57 "evalc((-1)^(1/4)),\nevalc(surd(-1,4)), evalc((
-1)&^(1/4));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%,&*$\"\"##\"\"\"F%F&*&
%\"IGF'F%F&F&,&F$#!\"\"F%F(F&F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 32 "evalc((-1)^(2/3)), (-1) &^(2/3);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6$,&#!\"\"\"\"#\"\"\"*&%\"IGF'\"\"$#F'F&F+F'" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 37 "evalc((-1)^(5/8)),evalc((-1)&^(5/8));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6$,&*$,&\"\"#\"\"\"*$F&#F'F&!\"\"F)#F*F&
*&%\"IGF',&F&F'F(F'F)F),&*$F.F)F+*&F-F'F%F)F)" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 35 "assume(n<0): n &^(3/5), n &^ (4/5);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6$,$*$,$%#n|irG!\"\"#\"\"$\"\"&F'*$F%#\"\"%F*" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "plot(x &^ (2/3), x = -1 .. \+
1);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 30 "plot(x &^ (3/5), x = -1 .. 1);" }}{PARA 13 "" 1 "" 
{TEXT -1 0 "" }}}}{SECT 0 {PARA 0 "" 0 "" {TEXT 26 9 "See also:" }
{TEXT -1 1 " " }{HYPERLNK 17 "^" 2 "^" "" }{TEXT -1 2 ", " }{TEXT -1 
1 " " }{HYPERLNK 17 "Fractional powers of negative numbers" 2 "Fractio
nal_powers_of_negative_numbers" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "sur
d" 2 "surd" "" }}}{SECT 0 {PARA 0 "" 0 "" {TEXT 26 24 "Maple Advisor D
atabase  " }{TEXT -1 14 "R. Israel 1998" }}}}{MARK "3 0 4" 0 }
{VIEWOPTS 1 1 0 1 1 1803 }