Jan 31, 2017 · To understand why the zeroth power works the way it does it's important that we properly define exponentiation. Exponentiation is the act of raising a number to the power of another number.

Feb 12, 2018 · But, coming to the original question, can $0^0$ defined to be $1$ just like $0!=1$? $ 0!=1$ makes sense but $0^0$ seems a little bit vague to me. Any help would be appreciated :)

Apr 29, 2015 · Why is any number to the zeroeth power equal to 1? I would think it would be equal to zero, since nothing multiplied by nothing is, well, I would think 0. But it is 1? Examples: $(-5)^0 = 1$; …

@Arturo: I heartily disagree with your first sentence. Here's why: There's the binomial theorem (which you find too weak), and there's power series and polynomials (see also Gadi's answer). For all this, …

The exponent $0$ provides $0$ power (i.e. gives no power of transformation), so $3^0$ gives no power of transformation to the number $1$, so $3^0=1$. Once you have the intuitive understanding, you …

I have been a witness to many a discussion about numbers to the power of zero, but I have never really been sold on any claims or explanations. This is a three part question, the parts are as follo...

The product of 0 and anything is $0$, and seems like it would be reasonable to assume that $0! = 0$. I'm perplexed as to why I have to account for this condition in my factorial function (Trying to learn …

Apr 23, 2021 · 0 Taking a shot in the dark: $10^3 = 10 * 10 * 10 = 1 (10 * 10 * 10)$ $10^2 = 1 (10 * 10)$ $10^1 = 1 (10)$ $10^0 = 1$ This isn't quite proofy enough, but seems to be reasonably convincing to …

16 I had the question of $0^ {-1}$ on a math test and I naturally assumed that this evaluates to zero, but from what I have seen from various sources it is equal to infinity which I do not quite understand. I …

When we write something like $\infty \cdot 0$, this doesn't directly mean anything; rather, it's shorthand for a certain type of limit, where the first part approaches infinity. Now, zero times anything …