Assigning a value to 0 0The rules of exponents tell us that if a is any number d...

Assigning a value to 0 0The rules of exponents tell us that if a is any number different from zero. They also tell us that if n is any positive number.

If we tried to extend these rules to include the case 0⁰ we would get conflicting results. The first rule would say whereas the second would say

We are not dealing with a question of right or wrong here.Neither rule applies as it stands, so there is no contradiction. We could, in fact, define to have any value we wanted as long as we could persuade others to agree.

What value would you like 0⁰ to have? Here is an example that might help you to decide. (See Exercise 2 below for another example.)

a. Calculate x ^x for x = 0.1,0.01, 0.001, and so on as far as your calculator can go. Record the values you get. What pattern do you see?

b. Graph the function for Even though the function is not defined for the graph will approach the y-axis from the right. Toward what y-value does it seem to be headed? Zoom in to further support your idea.