List questions from exponentiation

Published on 08 Apr 2026 - 19:33

329

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Refinements of the inequality $f(x)=x^{2(1-x)}+(1-x)^{2x}\leq 1$ for $0<x<0.5$

Published on 17 Apr 2026 - 10:25

237

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'Vandermonde-esque' matrix has nonzero determinant.

Published on 25 Mar 2026 - 17:28

272

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For which positive integers $x$, $y$ satisfy the following equation: $x^2 + y^2 = 2020$?

Published on 15 Apr 2026 - 16:41

99

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Can you take a fractional root of a number?

Published on 11 Apr 2026 - 15:50

227

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Partial proof by induction of the inequality : $(1-x)^{(2x)^n}+x^{(2(1-x))^n}\leq 1$

Published on 17 Apr 2026 - 3:37

49

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Why is $(e^{2πi})^i$ different from $(e^i)^{2πi}$

Published on 14 Apr 2026 - 10:21

31

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Exponentiation on a proof by induction

Published on 09 Apr 2026 - 0:18

192

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HowTo Rearrange The Piano Key Frequencies Formula

Published on 11 Apr 2026 - 15:18

91

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Evaluating difficult integral with exponentials

Published on 10 Apr 2026 - 9:11

188

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I need to prove that $(a^n)(b^n) = (ab)^n,$ where $a,b\in\mathbb N$. Proof by induction on $n \in \mathbb Z, n\geq 0$.

Published on 16 Apr 2026 - 6:53

74

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Definition of $x^{-a}$ and $x^{1/a}$

Published on 13 Apr 2026 - 14:14

118

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Why doesn't the graph of $y=\left(x^{1/2}\right)^{2}$ include negative $x$ values?

Published on 16 Apr 2026 - 17:42

111

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How do I solve $(1/4)^{x+1}+(1/4)^x=20$?

Published on 18 Apr 2026 - 11:41

27

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Mean/median/etc of a zero-mean random variable with exponent

Published on 12 Apr 2026 - 7:23

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Restrictions on exponential laws

Refinements of the inequality $f(x)=x^{2(1-x)}+(1-x)^{2x}\leq 1$ for $0<x<0.5$

'Vandermonde-esque' matrix has nonzero determinant.

For which positive integers $x$, $y$ satisfy the following equation: $x^2 + y^2 = 2020$?

Can you take a fractional root of a number?

Partial proof by induction of the inequality : $(1-x)^{(2x)^n}+x^{(2(1-x))^n}\leq 1$

Why is $(e^{2πi})^i$ different from $(e^i)^{2πi}$

Exponentiation on a proof by induction

HowTo Rearrange The Piano Key Frequencies Formula

Evaluating difficult integral with exponentials

I need to prove that $(a^n)(b^n) = (ab)^n,$ where $a,b\in\mathbb N$. Proof by induction on $n \in \mathbb Z, n\geq 0$.

Definition of $x^{-a}$ and $x^{1/a}$

Why doesn't the graph of $y=\left(x^{1/2}\right)^{2}$ include negative $x$ values?

How do I solve $(1/4)^{x+1}+(1/4)^x=20$?

Mean/median/etc of a zero-mean random variable with exponent

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