Is x to the 0th power 0 or 1?

Question

When x is 0, or perhaps 0 itself is considered the middle number, but I know that every number to the 0th power is one, I also know that zero to any power is 0, but what is zero to the 0th power? Is it zero or one. I am not sure, I know you can't divide zero by zero to make one, because anything to divided by zero is invalid. But divide zero by any number except for itself and it will always be zero. Is zero to the zeroth power zero, one, or undefined?

ignoramus · Accepted Answer

Zero is an exception to the rules of arithmetic.  It cannot be treated lightly, or at all, because it frequently results in a meaningless answer.  Just remember the few results that involve it, of which  an important one is  that any number to power 0 = 1.

If it helps, recall that to divide two numbers, let us say for example

(321^9)/(321^5)

you just need to subtract the powers, so (321^9)/(321^5) = 321^4.

So if you should have (321^9)/(321^9), then the answer is just
321^(9 - 9) = 321^0.  And, obviously 321^x/321^x is simply 1, whatever the value of x.  So the answer to ALL such problems is 1.

Krishnamurthy · Answer

x^0 = 1

az_lender · Answer

Zero to the zero power is undefined.  Anything else to the zero power is 1.

Puzzling · Answer

Any *non-zero* value raised to the power 0 is always 1.

x^0 = 1, as long as x ≠ 0

But if x = 0, the value of 0^0 is indeterminate.

? · Answer

0^0 is referred to as an indeterminate form, it can be anything.

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Is x to the 0th power 0 or 1?

5 Answers