You signed in with another tab or window. Reload to refresh your session.You signed out in another tab or window. Reload to refresh your session.You switched accounts on another tab or window. Reload to refresh your session.Dismiss alert
Describe the bug
The calculator can raise a negative number to a fractional rational power, which is mathematically wrong. The function g(x) = x^(1/n) is only defined on the ray [0; +∞), because the following property a^(m/n) = ⁿ√(a^m) works for only positive numbers a > 0
P. S. The calculator works fine with even denominators and returns an error. I guess, the reason is that computers cannot execute the square root of a negative number
Steps To Reproduce
Go to engineer mode
Execute (-8)^(1/3) or something else, where the base is negative and the power is fractional rational with an odd denominator
Get the answer
Expected behavior
The calculator has to return an error
Screenshots
last three images shows how it should be
Device and Application Information
OS Build: Windows 10.0.19045.5371.0
Architecture: X64
Application Version: 11.2411.1.0
Region: ru-RU
Dev Version Installed: False
Additional context
Some people think that a^(m/n) = ⁿ√(a^m) for any value of a, but it's wrong. Let me explain...
Let's assume that a^(m/n) = ⁿ√(a^m) works for any numbers...
(-8)^(1/3) = (-8)^(1/3)
We know that (2a)/(2b) = a/b, so 1/3 = 2/6
Let's rewrite one of the expressions in a different way (-8)^(1/3) = (-8)^(2/6)
It seems to be OK, so let's use the following property and rewrite the expression: a^(n/m) = ⁿ√(a^m) ³√(-8) = ⁶√((-8)^2) ³√(-8) = ⁶√64 -2 = 2
And this is why we can't raise negative numbers to a fractional rational power and why a^(m/n) = ⁿ√(a^m) doesn't work for negative numbers.
Now, let a be zero, then: 0^(-2/3) = ³√(0^(-2)) = ³√(1/0)
So this rule also doesn't work for a = 0
Requested Assignment
I'm just reporting this problem. I don't want to fix it.
The text was updated successfully, but these errors were encountered:
raven-xr
changed the title
Raising a negative number to a fractional rational power
The calculator can raise a negative number to a fractional rational power with an odd denominator
Jan 25, 2025
Describe the bug
The calculator can raise a negative number to a fractional rational power, which is mathematically wrong. The function
g(x) = x^(1/n)
is only defined on the ray[0; +∞)
, because the following propertya^(m/n) = ⁿ√(a^m)
works for only positive numbersa > 0
P. S. The calculator works fine with even denominators and returns an error. I guess, the reason is that computers cannot execute the square root of a negative number
Steps To Reproduce
Expected behavior
The calculator has to return an error
Screenshots
last three images shows how it should be
Device and Application Information
Additional context
Some people think that
a^(m/n) = ⁿ√(a^m)
for any value ofa
, but it's wrong. Let me explain...Let's assume that
a^(m/n) = ⁿ√(a^m)
works for any numbers...(-8)^(1/3) = (-8)^(1/3)
We know that
(2a)/(2b) = a/b
, so1/3 = 2/6
Let's rewrite one of the expressions in a different way
(-8)^(1/3) = (-8)^(2/6)
It seems to be OK, so let's use the following property and rewrite the expression:
a^(n/m) = ⁿ√(a^m)
³√(-8) = ⁶√((-8)^2)
³√(-8) = ⁶√64
-2 = 2
And this is why we can't raise negative numbers to a fractional rational power and why
a^(m/n) = ⁿ√(a^m)
doesn't work for negative numbers.Now, let
a
be zero, then:0^(-2/3) = ³√(0^(-2)) = ³√(1/0)
So this rule also doesn't work for
a = 0
Requested Assignment
I'm just reporting this problem. I don't want to fix it.
The text was updated successfully, but these errors were encountered: