Bite-sized knowledge for the hungrily curious
Oct19
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What is zero to the power of zero?

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The Answer

There’s no single correct answer to this question, so 00 is indeterminate. Arguments could be made for it to be 0, 1, or undefined. For calculation purposes, it’s officially defined as 1.

Depending on how you approach the question, there are multiple answers that can be reached, and they are all equally valid.

Zero to the power of any positive, real number is always zero. Following that logic, 0x = 0 no matter how close x gets to 0, which implies that zero to the power of zero could be zero.

On the other hand, zero to the power of zero could just as easily equal one, since any real number to the power of zero equals one.

There are certain fields of mathematics where mathematicians need an actual, numerical answer to this question. Instead of using either of the previous two methods (0x and x0), they combine them and see what xx approaches when x gets closer to zero. Using this, the answer they found the answer to be… 1!

Graph of y=xx | Generated using Desmos Graphing Calculator

There’s some degree of disagreement between mathematicians as to whether the answer is zero, one, or undefined, which mostly comes from different fields of math and different techniques.

In short, zero to the power of zero is defined to equal 1 when necessary, but there’s no distinct answer, and most calculators would give you undefined or indeterminate.

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