SOLUTION: (a). Evaluate 6^,5^0,4^0,3^0,2^0,and 1^0. If you are defining 0^0 what value would you give for 0^0? 0^0 is inderterminate expression. Based on your observation in in part (a) e

Algebra ->  Exponents -> SOLUTION: (a). Evaluate 6^,5^0,4^0,3^0,2^0,and 1^0. If you are defining 0^0 what value would you give for 0^0? 0^0 is inderterminate expression. Based on your observation in in part (a) e      Log On


   

Question 168709: (a). Evaluate 6^,5^0,4^0,3^0,2^0,and 1^0. If you are defining 0^0 what value would you give for 0^0?
0^0 is inderterminate expression. Based on your observation in in part (a) explain why you think 0^0 is indeterminate.
Found 2 solutions by vleith, jim_thompson5910:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
See this --> http://mathforum.org/dr.math/faq/faq.number.to.0power.html
x^0 where x is anything except 0 is defined as 1
You can see that x%5E0+=+x%5E%28y-y%29
x%5E%28y-y%29+=+%28x%5Ey%29%2F%28x%5Ey%29=+1 for all x!=0
this works for all x except x=0. If x=0 then term (0^y) in the denominator is undefined

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
ANY number (except 0) to the zeroth power is ALWAYS 1. So 1%5E0=1, 2%5E0=1, 3%5E0=1, 4%5E0=1, 5%5E0=1, 6%5E0=1, etc.


Now why did we exclude zero? It turns out that zero to ANY power (except 0) is 0. So 0%5E1=0, 0%5E2=0, 0%5E3=0, 0%5E3=0, 0%5E4=0, 0%5E5=0, etc.


So the question is: what is 0%5E0 ??? Is is 1 (since the exponent is 0) or is it 0 (since the base is 0)? Since this contradiction occurs (and a few other reasons), this means that 0%5E0 is an indeterminate expression.