What is the value of 0 to the power of 0 ?

Answer 1

It does not exist.

Answer 2

1

Answer 3

1

Answer 4

If y approaches 0 as x approaches 0 from above, then xy may approach any nonnegative value, or fail to converge. If y = log(a)/log(x), then xy = a for all positive x. The function xy is not continuous in (x,y)=(0,0). So 00 cannot be determined simply by continuity. (See indeterminate form).

However, if the plane curve along which the point (x,y) moves towards (0,0) is bounded away from tangency to the y-axis, then the limit is one. Thus it may be said that, the limit is almost always 1.

Furthermore, if the function y=f(x) or the inverse function x=f−1(y) is a nonzero analytic function with f(0)=0, then limx→0 xy = 1. (Note that neither y=log(a)/log(x) nor x=a1/y are analytic around x=0).

For purposes such as those of combinatorics, set theory, the binomial theorem, and power series, one should also take 00 = 1.

From the combinatorial point of view, the number nm is the size of the set of functions from a set of size m into a set of size n. If both sets are empty (size 0), then there is just one such mapping: the empty function.

A striking instance is the fact that the Poisson distribution with expectation 0 concentrates probability 1 at 0; which agrees with the formula for the probability mass function of the Poisson distribution only if 00 = 1.

The consistent point of view incorporating these aspects is to define


0 raised to the power of 0 = 1

Answer 5

It is undefined.

Think about it this way: 5^2 / 5^2 = 5^0 = 1 (in order to divide, you subtract the exponents)

but 0^2 / 0^2 would have 0 as a denominator. You can never divide a number by 0, thus, 0^0 does not exist.

Answer 6

any number to the power 0 is 1.

Answer 7

You can't take 0 to any power. Any other number to the power of 0 is 1.

Answer 8

1, because any number to the power of 0 equals one

Answer 9

0 of course

Answer 10

0 dude

Answer 11

-1