Can someone explain this fallacy?

[rotund needle]

does the third step follow how powers work?

[deft vale]

I'm not sure

[rotund needle]

(-1) ^ 2 * 1/2 = ((-1)$^2$)$^1/2$

[deft vale]

Cause of the error: raising to a fractional power is only defined for non-negative numbers

I don't understand what this means ^

Anyone? please

[rotund needle]

to the power of

$5^4$

[rustic depot]

doated

[deft vale]

I still don't understand, i'm sorry

[rotund needle]

its a way to type to the power of

[thin venture]

Square root of 1 is equal to ±1, not 1

[cunning vapor]

in some cases square root as seen as a function

as the principal root

in which case you have to be kinda careful

another fallacy is 2ln(-1) =/= ln((-1)^2)

many rules don’t apply to negative numbers

[deft vale]

Is there any rule to this?

[cunning vapor]

nth root has n values for example the 4th root of 1 is 1, -1, i, -i

[deft vale]

nth? Sorry for the questions

[cunning vapor]

um

4th root has 4 values

5th root has 5 values

etc

[deft vale]

ohh

[cunning vapor]

square root is also called 2nd root

[deft vale]

So because sqrt 1 is not only = 1, but and = -1, this is fallacy, right?

[deft vale]

Could you take a look on something

[cunning vapor]

imo this is the real reason

but yes saying it’s +- 1 solves it

[cunning vapor]

hm?

[deft vale]

So, this is a fallacy, trying to prove that e = m. The mistake is that sqrt is cancelled incorrectly, right?

[cunning vapor]

correct

this is like saying (5-3)^2 = (5-7)^2 so 3 = 7

[deft vale]

Is there a way to word it smooth? I need to be ready to explain it

[cunning vapor]

remember that square root of x^2 is not x, it’s |x| (or +-x, not the same but you can choose either to say)
so that step is just wrong

[deft vale]

Thank you, appreciate it very much.