what is:
0^{0}
ie zero to the power zero
and why ? what is:
0^{0}
ie zero to the power zero
and why ? @Mathematics

Question

anonymous · Answer

http://en.wikipedia.org/wiki/Exponentiation#Zero_to_the_zero_power

anonymous · Answer

1

anonymous · Answer

according to some Calculus textbooks, 0^0 is an ``indeterminate form''. When evaluating a limit of the form 0^0, then you need to know that limits of that form are called ``indeterminate forms'', and that you need to use a special technique such as L'Hopital's rule to evaluate them. Otherwise, 0^0 = 1 seems to be the most useful choice for 0^0.

anonymous · Answer

It can be sometimes 1 or indeterminate, it really depends on the person defining it. See the Wikipedia article for discussion.

asnaseer · Answer

$$x ^{a}*x ^{b}=x ^{a+b}$$so if a is 1 and b is -1 we get$$x ^{1}*x ^{-1}=x ^{1-1}$$$$x * 1/x = x ^{0}$$$$x/x=x ^{0}$$$$1=x ^{0}$$

asnaseer · Answer

set x=0 in the above and you get$$0 ^{0}=1$$

yash2651995 · Answer

a^0=1......(1)
0^b=0......(2)
if a=0, b=0
which equation should I choose?
(1) or (2)

asnaseer · Answer

from my example above$$x ^{0}=x/x$$so you can take limits to get$$0 ^{0}=\lim_{x \rightarrow 0}(x/x)=1$$

asnaseer · Answer

yash2651995 your equation above where you said 0^b = 0 is ONLY true for b > 0.
e.g. if b=-1 you would get$$0 ^{-1}=1/0=\infty$$

asnaseer · Answer

so for positive n:$$0 ^{n}=0$$$$0 ^{0}=1$$$$0 ^{-n}=\infty$$

zarkon · Answer

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