# Knowledge Base

## Solution 11805: Negative Exponents of Zero Return Inconsistent Answers on the TI-89 Family, TI-92 Family and Voyage™ 200.

### Why do the TI-89 family, TI-92 family and Voyage 200 return inconsistent answers when zero is raised to the power of negative numbers?

The following is an explanation of why the TI-89 family, TI-92 family and Voyage 200 display "undef" for odd negative exponents and infinity for even negative exponents for a base of zero.

Functions of the form 1/(x-a)^(odd power), for real x and real a, have an odd-order pole at x = a. The sign changes as x crosses the pole, and limit(1/(x-a)^(odd power),x,a) = undef (the limit from the right has different sign from the limit from the left).

Functions of the form 1/(x-a)^(even power), for real x and real a, have an even-order pole at x = a. The limit(1/(x-a)^(even power),x,a) = infinity (the limit from the right = infinity, and the limit from the left = infinity).

On the TI-89 family, TI-92 family and Voyage 200 the following occurs when a zero base is raised to a negative exponent:

0^-1 solution "undef"
0^-2 solution infinity
0^-3 solution "undef"
0^-4 solution infinity
etc...

The answer should always be undefined since (0/1)^-n is (1/0)^n.