Remember that Excel and almost all other computer programs do math
numerically in binary, not algebraically.

Rational numbers of the form 1/n (where n is an integer) can only be
exactly represented in Excel if n is an integer power of 2. Otherwise
1/n must be approximated. Similarly, rational numbers of the form m/n
can only be exactly represented if n/g is an integer power of 2, where g
is the greatest common divisor of both m and n. Otherwise m/n must be
approximated. When Excel is asked to raise a negative number to a power
that is close enough to 1/n for some integer n, then the power routine
makes a guess that the number is an approximation to 1/n. This guess
may be wrong, but the developers were willing to take that chance for
numbers of the form 1/n, though not for general rational numbers m/n.
It is a design decision.

Presumably you do know whether the power is rational or not, where Excel
can only guess. When it is rational, you can help Excel and insure that
you get the answer you want by restructuring the calculation so that
Excel is looking at ...^(1/n) not ...^(m/n).

Note that even algebraic software may take the primary branch to be
complex rather than real. For example, in Maple
simplify((-3)^(-2/3))
is complex. Excel's Analysis ToolPak has functions for complex arithmetic
http://groups.google.com/groups?selm...0no_e-mail.com

Jerry

Dailoc Nguyen wrote:


Thanks for quick reply.
We have some reply that are not quite getting along with each other.
Mathematically, you can take an odd root of a negative number. Also
those 2 statements are equivalent mathematically [(-3)^(-2/3) =
((-3)^(-2))^(1/3)] and should not yield an imaginary number.
This question seems to be very interesting.

Lmn.