**Question: Why does something in the power of zero equal one.? (x<sup>0</sup> = 1)**

While some believe this is a definition, the definition can be proved by using the calculation rules.:

  * (x<sup>a</sup>) / (x<sup>b</sup>) = x<sup>(a-b)</sup>

While this may not look like something that can explain the x<sup>0</sup>=1 problem, bear with me, I will come to that in a second. When working with formulas one must accept that sometimes the right hand side equals the left hand side of the equation, hence the equation mark. And so, we have to assume the above formula is correct otherwise someone has told me something wrong, and I will stand corrected ;-).  

 Fortunately I know it to be otherwise. Here comes the proof for x<sup>0</sup> = 1


First we need to get the right hand side to become x<sup>0</sup> - so we set <sup>a</sup> and <sup>b</sup> to the same number, in this case 2 - but it will work with anything really as long as a minus b gives 0. For your enjoyment we also set x to something, we set that to 3. 

Right hand side formula now reads: 3<sup>(2-2)</sup>, And as with all formula's, shorter is better, <sup>2-2</sup> = <sup>0</sup>, and so we can write 3<sup>0</sup>.

We can now write out our formula:

  * (3<sup>2</sup>) / (3<sup>2</sup>) = 3<sup>0</sup>
Just like before, shorter is better - and now we can take the left hand side and shorten that one:
  * (9) / (9) = 3<sup>0</sup>
And then shorten it some more
  *1 = 3<sup>0</sup>

Presto - you now also know why x<sup>0</sup> = 1 and not 0 :)