(35s) y^x for y < 0 and x < 1 (complex roots)

[Dieter]

(04-29-2016 06:28 AM)brianddk Wrote:  Howdy,
I stumbled across a thread a while back discussing the following well documented behavior on the 35s

Code:

2
+/-
3
y^x
LASTx
1/x
y^x
**INVALID y^x

Obviously if 'x' can be expressed as a rational number and if both the numerator and the denominator are both odd, then the sign of y is irrelevant and it will carry through the exponentiation.

According to this rule –8^(3/5) should work, but it doesn't => INVALID y^x.

I think it's much simpler: the error in your example occurs because you want the calculator to evaluate (–8)^0,333333333333.
But this does NOT equal (–8)^(1/3), so no (real) result exists.

That's why there is a XROOT function (x√y, on the K key). –8 [ENTER] 3 [x√y] returns –2, as expected. Here no errors occur for y<0 if x is an odd integer.

So instead of –8^(3/5) you can use –8^3 = –512 and then the 5th root of this yields –3,4822.

Dieter