## 101Ryan101 Group Title Medals for ones who prove: 0^0 = 1 (I wrote the last one wrong) :/ 3 years ago 3 years ago

1. angela210793 Group Title

every no in exponent 0 is =1.....idk how to prove tht though :(...my teacher has never asked me tht and she has never proved tht to me O.o...sorry :/

2. ragnarok23 Group Title

There's a combinatorial argument. Consider trying to arrange 0 objects in a line - this is 0^0. There's exactly one way to do this: do nothing.

3. 101Ryan101 Group Title

Is there an algebraic proof involving an equation?

4. 101Ryan101 Group Title

It seems more intuitive that the answer would be 0 to me, that's all.

5. joemath314159 Group Title

you could use the binomial theorem, and the fact that 0! = 1 $(x+y)^n = \left(\begin{matrix}n \\ 0\end{matrix}\right)x^n+\left(\begin{matrix}n \\ 1\end{matrix}\right)x^{n-1}y+\ldots+\left(\begin{matrix}n \\ n\end{matrix}\right)y^n$ $=\sum_{i=0}^{n}\left(\begin{matrix}n \\ i\end{matrix}\right)x^{n-i}y^i$ Let n = 0, and y = -x, we end up with: $(x-x)^0 = \left(\begin{matrix}0 \\ 0\end{matrix}\right)x^0(-x)^0 \iff 0^0 = 1$

6. jimmyrep Group Title

3^8 / 3^8 = 1 = 3^(8-8) = 3^0

7. 101Ryan101 Group Title

Thanks Joe, I don't understand that proof but it helps to know that it's beyond my level at this point.

8. joemath314159 Group Title

>.< im sry, is there a certain part of it you dont understand? i only have 15 mins till my next class, but im down to try and explain.

9. 101Ryan101 Group Title

no, it's fine.. I'm serious.. thax... Just wanted to look into this and get some feedback is all..

10. 101Ryan101 Group Title

Jimmyrep! nice! that's a good one for me to grasp..