What is 0 to the power of 0?

Like the title says, what is 0 to the power of 0? Anything to the power of 0 is always 1, but any power of 0 is always 0.

#Algebra

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Well, $0^0$ is actually undefined but many people have been arguing about it on this website for ages i suppose :) just note that we arrived at $a^0=1$ for any $a$ is because we defined $a^{m-n}=\frac{a^m}{a^n}$ . Plugging in $m=n$ gives $a^0=\frac{a^m}{a^m}=1$ . But if $a=0$ , then the fraction simplifies to $\frac{0}{0}$ . You can easily see it’s undefined.

Jeff Giff - 1 week, 5 days ago

Ah, thank you!

Alan Vu - 1 week, 5 days ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$