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What is 0^0? - Today's Algebra Books

Michael Huber and V. Frederick Rickey


Pick up a high school mathematics textbook today and you will see that 00 is treated as an indeterminate form. For example, the following is taken from a current New York Regents text [6]:

We recall the rule for dividing powers with like bases:

xa/xb = xa-b (x not equal to 0) (1)

If we do not require a > b, then a may be equal to b. When a = b:

xa/xb = xa/xa = xa-a = x0



xa / xa = 1 (3)

Therefore, in order for x0 to be meaningful, we must make the following definition:

x0 = 1 (x not equal to 0) (4)
Since the definition x0 = 1 is based upon division, and division by 0 is not possible, we have stated that x is not equal to 0. Actually, the expression 00 (0 to the zero power) is one of several indeterminate expressions in mathematics. It is not possible to assign a value to an indeterminate expression.


Editor's note: This article was published in March of 2008.

Michael Huber and V. Frederick Rickey, "What is 0^0? - Today's Algebra Books," Convergence (July 2012)