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www.math.hmc.edu/funfacts/ffiles/10005.3-5.shtml

Zero to the Zero Power: It is commonly taught that any number to the zero power is 1, and zero to any power is 0. But if that is the case, what is zero to the zero power? Well, it is undefined (since x y as a function of 2 variables is not continuous at the origin). But if it could be defined, what "should" it be? 0 or 1?

en.wikipedia.org/wiki/Zero_to_the_power_of_zero

Zero to the power of zero, denoted by 0 0, is a mathematical expression with no agreed-upon value. The most common possibilities are 1 or leaving the expression undefined, with justifications existing for each, depending on context.

medium.com/i-math/the-zero-power-rule-explained-449b4bd6934d

The “ Zero Power Rule” Explained. Brett Berry Blocked Unblock Follow Following. Feb 18, 2016. Exponents seem pretty straightforward, right? Raise a number to the power of 1 means you have one ...

www.solving-math-problems.com/exponent-rules-zero.html

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The zero exponent rule states that any term with an exponent of zero is equal to one. This lesson will go into the rule in more detail, explaining how it works and giving some examples.

Zero to any positive exponent equals zero. So, what happens when you have zero to the zero power? If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

mathforum.org/dr.math/faq/faq.number.to.0power.html

While the above argument might help convince your intuitive side that any number to the zero power is 1, the following argument is a little more rigorous. This proof uses the laws of exponents. One of the laws of exponents is: n^x --- = n^(x-y) n^y for all n, x, and y. So for example,

www.homeschoolmath.net/teaching/zero-exponent-proof.php

You are here: Home → Articles → Zero exponent proof Proof that (-3) 0 = 1 How to prove that a number to the zero power is one. Why is (-3) 0 = 1? How is that proved? Just like in the lesson about negative and zero exponents, you can look at the following sequence and ask what logically would come next:

www.homeschoolmath.net/teaching/negative_zero_exponents.php

Is there a general rule for doing all exponents, or does a negative exponent have nothing in common with positive exponents? n to 0 power Why any number raised to the zero power is equal to one. Decimal Exponents Can you have exponents that are decimals? Meaning of Irrational Exponents But where do irrational exponents fit in?

en.wikipedia.org/wiki/Exponentiation

Zero exponent. Any nonzero number raised to the 0 power is 1: = One interpretation of such a power is as an empty product. The case of 0 0 is more complicated, and the choice of whether to assign it a value and what value to assign may depend on context. For more details, see Zero to the power of zero.

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