why does 0 to the power of 0 equal 1?
In: 97
Lots of correct answers here. 0^0 is undefined.
However, an interesting way to look at equations is to analyze what happens to functions when you play with the numbers. If you load up a graphing calculator, you can plot functions that include 0^0. The simplest function to understand this is [x^x](https://www.wolframalpha.com/input?i=x%5Ex). The graph gets really close to 1 as x approaches 0, but the line never touches. It gets infinitely close, but it never touches.
For this reason, it is perfectly valid to say that the limit as x approaches zero is 1. The the exact value, however, is undefined. You can plug other functions into a graphing calculator that include 0^0, and you will find that all of them will have the same limit of 1, yet the line never touches the y axis.
Latest Answers