List questions from exponentiation

Published on 24 Dec 2015 - 3:57

145

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How many times is $3^{20} + 3^{22}$ greater than $3^{20}$

Published on 24 Dec 2015 - 7:22

88

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How to handle indices with fractional degree?

Published on 24 Dec 2015 - 7:36

189

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Can't solve this exponential equation: $5^{x+1}-3\cdot 5^{x-1} - 6\cdot 5^x+10 = 0$

Published on 24 Dec 2015 - 17:09

82

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Problem with custom made natural log and power functions

Published on 27 Dec 2015 - 6:25

334

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Prove $e^{i\alpha\hat{X}}=\cos(\alpha)I+i\sin(\alpha)\hat{X}$ if $\hat{X}^{2}=I$.

Published on 04 Apr 2026 - 3:54

49

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Square of a Sequence of Numbers

Published on 01 Jan 2016 - 4:39

96

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How is exponentiation defined?

Published on 02 Jan 2016 - 21:10

129

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Let $0<a<1$, for which $x>0$ is $x^{a^x} = a^{x^a}$ true.

Published on 03 Jan 2016 - 1:07

949

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Which is larger, $\sqrt[2015]{2015!}$ or $\sqrt[2016]{2016!}$?

Published on 04 Apr 2026 - 8:41

51

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Degree of a root term?

Published on 04 Jan 2016 - 16:55

17.1k

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Why does the minimum value of $x^x$ equal $1/e$?

Published on 04 Jan 2016 - 20:21

104

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How to derive that for every real $y > 0$, for every positive real $z \neq 1$, there is a $x \in \mathbb{R}$ such that $y=z^x$.

Published on 06 Jan 2016 - 15:12

286

Views

How to define matrix power

Published on 07 Jan 2016 - 14:52

115

Views

Finding the function that would describe this:

Published on 26 Mar 2026 - 12:51

List Question

How to find $a^b$, where $a$ and $b$have more than $10$ digits?

How many times is $3^{20} + 3^{22}$ greater than $3^{20}$

How to handle indices with fractional degree?

Can't solve this exponential equation: $5^{x+1}-3\cdot 5^{x-1} - 6\cdot 5^x+10 = 0$

Problem with custom made natural log and power functions

Prove $e^{i\alpha\hat{X}}=\cos(\alpha)I+i\sin(\alpha)\hat{X}$ if $\hat{X}^{2}=I$.

Square of a Sequence of Numbers

How is exponentiation defined?

Let $0<a<1$, for which $x>0$ is $x^{a^x} = a^{x^a}$ true.

Which is larger, $\sqrt[2015]{2015!}$ or $\sqrt[2016]{2016!}$?

Degree of a root term?

Why does the minimum value of $x^x$ equal $1/e$?

How to derive that for every real $y > 0$, for every positive real $z \neq 1$, there is a $x \in \mathbb{R}$ such that $y=z^x$.

How to define matrix power

Finding the function that would describe this:

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