Questions on Algebra: Exponents and operations on exponents answered by real tutors!

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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.
: (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.

Answer by vleith(1235) 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^0 = x^(y-y)
x^(y-y) = (x^y)/(x^y)= 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
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.
: (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.

Answer by jim_thompson5910(9897) About Me  (Show Source):
You can put this solution on YOUR website!
ANY number (except 0) to the zeroth power is ALWAYS 1. So 1^0=1, 2^0=1, 3^0=1, 4^0=1, 5^0=1, 6^0=1, etc.


Now why did we exclude zero? It turns out that zero to ANY power (except 0) is 0. So 0^1=0, 0^2=0, 0^3=0, 0^3=0, 0^4=0, 0^5=0, etc.


So the question is: what is 0^0 ??? 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 0^0 is an indeterminate expression.