Linked Questions
11 questions linked to/from What Is Exponentiation?
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Dimensions (squared, cubed, and more!!) [duplicate]
I know that when you square something you can visualize it as a 2d square. When you cube it you can visualize it as a 3d cube.
For example:
2^2 -- a 2 by 2 square
2^3 -- a 2 by 2 by 2 cube
I've ...
1
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1
answer
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The concept of an real irrational power [duplicate]
One can understand the concept of natural power, as $x^n$, being a product of a number by itself $n$ times:
$$x^n=\underbrace{x\cdot x\cdot\dotsb\cdot x}_n$$
We can also get the idea of a rational ...
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1
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What is the general definition of exponentiation? [duplicate]
The definition of exponentiation is commonly defined as:
$$x^n:=\underbrace{x\cdot x\cdot x\cdot ...\cdot x}_\text{n times}$$
when $n \in \mathbb N $.
Given that, what is the definition when $n \notin ...
225
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10
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What does $2^x$ really mean when $x$ is not an integer?
We all know that $2^5$ means $2\times 2\times 2\times 2\times 2 = 32$, but what does $2^\pi$ mean? How is it possible to calculate that without using a calculator? I am really curious about this, so ...
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6
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Why is exponentiation defined as $x^y=e^{\ln(x)\cdot y}$?
There are many curves that extend integer exponentiation to larger domains, so why was this one chosen?
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Which general physical transformation to the number space does exponentiation represent?
Addition and multiplication may be defined in two ways, one specific and one general:
Addition
specific: addition is repeated incrementation.
This is specific and sub-optimal as while $2 + 4$ is ...
3
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2
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958
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Is there a deeper meaning when a number is squared? [closed]
In my opinion, math is about more than just memorizing equations, it's about numbers that are built in a way that represents our understanding of something.
So I ask this, what does it mean ...
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Trying to _really_ understand exponents...
I am a programmer, but grew up with a pretty weak math education. While I can cobble together enough understanding to build something like these charts solo from raw data, my level of true math ...
3
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2
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Is $(-3)^\sqrt{2}$ a real number ? If it a complex number, then what is its $a+bi$ form?
Is this a real number? If it a complex number, then what is its $a+bi$ form?
$$(-3)^\sqrt{2}$$
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3
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How do Mathematicians determine when to use the constant $e$?
I'm only an undergrad so sorry if this is a dumb question, but I was studying Poisson distribution and it struck me that so many models involve "e". So it got me wondering; how/when/where/why do they ...
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Derive the p-test if p is an irrational number
I would like some help with this problem. I've been given that we have a $k^p$ s.t. $p$ is irrational and $k$ is a positive integer satisfies the following:
$k^r\lt k^p$ if $r$ is positive and ...