# Zero raised to zero

Something’s not working the way it seems like it should.

When I created this activity:
Exploring Exponent Properties II: Division of Powers and Negatives Exponents

I start with having students look at various numbers raised to the zero power.

I created a slide where students summarized (slide 4) and had created a follow-up slide where students would check 0^0. The Desmos Scientific Calculator provided an answer of 0, but I expected an error or undefined answer. I deleted that slide to avoid student confusion.

Here’s the link to the page, dashboard, or activity:

And here are some screenshots or a video:

I will do a little bit of a reply to myself…
It looks like there is disagreement among mathematicians as to the exact value of 0^0, so perhaps this shouldn’t be considered a bug per se…
Here are a couple of sources:
Wikipedia

MAA publication with some history and a proposition by the authors.

I will admit that I found the series example compelling for a justification that 0^0=1, but the concept still doesn’t quite settle with me correctly.

The value of 0^0 is one of those questions that always leads to interesting discussions. There some good arguments in favor of it being 0, 1, or undefined, depending very much on how you think about exponentiation in whatever context you’re using. Since all of those answers are “right” in some sense, at the end of the day the value of 0^0 just has to be a mathematical convention. We’ve actually gone back and forth on this point a bit (we reported 0^0 as undefined for a short period), but ultimately we think that 0^0=1 is the most lovely and useful convention, and the one most favored by mathematicians. Mostly because it preserves some beautiful theorems (like the binomial theorem, for instance) without introducing special cases.
We tend to point people to this article http://www.askamathematician.com/2010/12/q-what-does-00-zero-raised-to-the-zeroth-power-equal-why-do-mathematicians-and-high-school-teachers-disagree/, which very nicely lays out the arguments in favor of each position.
Hope this makes sense and please let us know if you have other questions.

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