Raising a negative number to a fractional power
Describe the bug
The calculator can raise a negative number to a fractional power, which is mathematically impossible. . 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. 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
- 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.
Source: microsoft/calculator