# Questions tagged [exponentiation]

Questions about exponentiation, the operation of raising a base $b$ to an exponent $a$ to give $b^a$.

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### Can the 0 power rule be conceptualized?

A review of the rule that $n^0$ is always 1, when n is not 0, has made me question if all math rules can be visualized or conceptualized with a general intuition gained from viewing the natural world. ...
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### What is the smallest value of n such that an algorithm running at 100*n^2 operates faster than 2^n ? [How to figure out without brute force]

Okay, so I needed to find the smallest value of n such that algorithm 100*n^2 is faster than 2^n. [what I have tried] So, I instantly thought '0'. But, I then realized it can't be 0, 0 implies that ...
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### Numerically stable evaluation of $x^{n!}$

Given that $x$ is a real number with property $0 < x < 1$ and $n$ upto $4000$ Is there a good way to decompose the n! into steps for multiplying x?
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### Intuitive understanding of Euler's Formula

Thanks for reading! In this link... https://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/ ...Euler's formula is explained pretty well. I understand that multiplying a ...