What is 0 to the 0?

Here's my understanding of it, Melody......

11 / 0     is "undefined" because we can't multiply anything by 0 in the denominator to return the "11"  in the numerator 

But.....consider......

0 / 0

We could multiply the denominator by anything to return the 0 in the numerator....thus....this is "indeterminate"....we can't determine  exactly what this "thing"  is......

It might be "pi"...it might be "10"....it might be "3.45612".......etc.

It is undefined

To see why Melody's answer is true......consider  the following where  n is non-zero

0ⁿ /  0^{n   =}

0^{n-n  =}

0⁰

But....what's the problem????  .....Note that......in the fraction above, the denominator 0ⁿ  = 0 .....and we can't divide by 0.......

[It's actually more appropriate to term this situation,  "indeterminate" ]

But that number n must be strictly greater than 0, because you can't have 0 to a power less than (or equal to) 0.

What is the difference between undefined and indeterminate Chris ?

Are they interchangable terms?

ok thanks Chris :)