Question

What is wrong with the reasoning in $(-1)^ \frac{2}{4} = \sqrt[4]{(-1)^2} = \sqrt[4]{1} = 1$ and $(-1)^ \frac{2}{4} = (-1)^ \frac{1}{2} = i$?

score 304 · Answer 1 · 2018-07-23 07:20:26

304

Views

What is wrong with the reasoning in $(-1)^ \frac{2}{4} = \sqrt[4]{(-1)^2} = \sqrt[4]{1} = 1$ and $(-1)^ \frac{2}{4} = (-1)^ \frac{1}{2} = i$?

Published on 23 Jul 2018 - 7:20

score 83 · Answer 2 · 2018-07-26 09:04:16

83

Views

How to find the least positive $K$ such that $N^K \equiv 1 \pmod{P}$ where $P$ is prime and $P$ doesn't divide $N$?

Published on 26 Jul 2018 - 9:04

score 133 · Answer 3 · 2018-07-26 12:15:24

133

Views

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Published on 26 Jul 2018 - 12:15

score 2.1k · Answer 4 · 2018-07-26 15:21:42

2.1k

Views

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score 117 · Answer 5 · 2018-07-28 21:42:51

117

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score 45 · Answer 6 · 2018-07-29 19:18:11

45

Views

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score 113 · Answer 7 · 2018-07-30 14:27:29

113

Views

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score 34 · Answer 8 · 2018-07-30 20:28:37

34

Views

Solving $KL^{2C} - LC^{2C} = (B-C)C^{2C} - C^{2C}(T+KG^2) - KP^2$ for $L$

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score 83 · Answer 9 · 2018-07-31 07:58:45

83

Views

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2k

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540

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score 862 · Answer 12 · 2026-03-25 17:36:08

862

Views

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score 59 · Answer 13 · 2018-08-04 13:34:54

59

Views

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score 90 · Answer 14 · 2018-08-08 01:58:06

90

Views

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Published on 08 Aug 2018 - 1:58

score 482 · Answer 15 · 2026-03-25 12:46:13

482

Views

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Published on 25 Mar 2026 - 12:46

List Question

What is wrong with the reasoning in $(-1)^ \frac{2}{4} = \sqrt[4]{(-1)^2} = \sqrt[4]{1} = 1$ and $(-1)^ \frac{2}{4} = (-1)^ \frac{1}{2} = i$?

How to find the least positive $K$ such that $N^K \equiv 1 \pmod{P}$ where $P$ is prime and $P$ doesn't divide $N$?

What's the formula for producing these series?

Between any two powers of $5$ there are either two or three powers of $2$

Exponential decay of the function

Factoring a number in the format $2^x + 2^y...$, etc.

Asymptotics to $f(n) = \int_0^1\bigl ( \frac{ \operatorname{li}(x)}{x} \bigr)^{2n + 1} \,(x-1) \, dx $

Solving $KL^{2C} - LC^{2C} = (B-C)C^{2C} - C^{2C}(T+KG^2) - KP^2$ for $L$

A Question About Square Roots And Exponent Laws

Can you prove the power rule for irrational exponents without invoking $e$?

Estimating the value of $\ln2$ using $e^3$ and $2^{10}$

GCD of exponents

Is it possible to graph $f(x) = (-2)^x$?

How to calculate modulus of remainder when a large number is divided by other.

$A$ is diagonalizable, then exists $B^3=A$

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