List questions from exponentiation

Published on 14 Apr 2026 - 1:53

36

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What is wrong in my calculation ($x^{-1} \cdot \sqrt[3]{x} = ?$)?

Published on 14 Apr 2026 - 8:17

557

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Proof for Perfect $n^{th}$ power.

Published on 11 Apr 2026 - 14:25

48

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Intuition for $e$ and natural logs

Published on 14 Apr 2026 - 17:20

74

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Prove that :$f(a^2)+f(b^2)+f(c^2)\leq f\left(\frac{1}{4}\right)+f\left(\frac{1}{4}\right)+f(0)$ where $f(x)=\sqrt{\frac{1+\sqrt{1+x}}{x^x}}$

Published on 14 Mar 2026 - 14:15

27

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Can always roots be transformed into exponents?

Published on 23 Apr 2026 - 21:15

113

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Optimization of the exponential of the decision variable $x$

Published on 10 Apr 2026 - 23:42

205

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Image of domain under map $f(z) = z^6$?

Published on 17 Apr 2026 - 9:24

97

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Prove the inequality $\ln\left(\Gamma(x^x+1)\right)< x^x\ln\left(\Gamma(x+1)\right)$ for $0<x<1$

Published on 17 Apr 2026 - 16:04

65

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$a \in \mathbb{R}$ and $a^7, a^{12} \in \mathbb{Q}$. Prove that $a \in \mathbb{Q}$.

Published on 17 Apr 2026 - 7:02

32

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What is an example of zero exponent in nature?

Published on 10 Apr 2026 - 8:19

318

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Again on Clausen paradox

Published on 11 Apr 2026 - 11:59

114

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$m^n$ has exactly $9$ digits, all of these digits are distinct.

Published on 16 Apr 2026 - 22:31

44

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Using modular arithmetic in exponent

Published on 12 Apr 2026 - 21:23

143

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Conjecture: $a^{(2(1-a))^{\frac{1}{n}}}+b^{(2(1-b))^{\frac{1}{n}}}+c^{(2(1-c))^{\frac{1}{n}}}+\frac{c}{n}\leq 1$

Published on 16 Apr 2026 - 19:50

List Question

How do I verify if $2^{35} \equiv 1 \pmod{71}$ is true or not?

What is wrong in my calculation ($x^{-1} \cdot \sqrt[3]{x} = ?$)?

Proof for Perfect $n^{th}$ power.

Intuition for $e$ and natural logs

Prove that :$f(a^2)+f(b^2)+f(c^2)\leq f\left(\frac{1}{4}\right)+f\left(\frac{1}{4}\right)+f(0)$ where $f(x)=\sqrt{\frac{1+\sqrt{1+x}}{x^x}}$

Can always roots be transformed into exponents?

Optimization of the exponential of the decision variable $x$

Image of domain under map $f(z) = z^6$?

Prove the inequality $\ln\left(\Gamma(x^x+1)\right)< x^x\ln\left(\Gamma(x+1)\right)$ for $0<x<1$

$a \in \mathbb{R}$ and $a^7, a^{12} \in \mathbb{Q}$. Prove that $a \in \mathbb{Q}$.

What is an example of zero exponent in nature?

Again on Clausen paradox

$m^n$ has exactly $9$ digits, all of these digits are distinct.

Using modular arithmetic in exponent

Conjecture: $a^{(2(1-a))^{\frac{1}{n}}}+b^{(2(1-b))^{\frac{1}{n}}}+c^{(2(1-c))^{\frac{1}{n}}}+\frac{c}{n}\leq 1$

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