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I just discovered this surprising feature on the Casio fx-5000F, visually nice but somehow functionally useless:

On the keyboard, there's not only the "x^y" function but also a "x^n" function !

e.g. on keying 2.67^13, and for the same result,
using the "x^y" function displays "2.67xy13",
but using the "x^n" function displays 2.6713 !

I think it's related to its large character set (Uppercase and lowercase alphabet, greek letters, physical constants) and formula programming type letting it calculate input as compact as "ax2+bx+c"

Did you ever see such a "x^n" function on a calculator ?
According to the manual "x^n" is specifically for positive integer powers, while "x^y" is for real numbers. I don't have one of these calculators, but I assume that you'll get an exact integer result from "x^n" always.
As a sideline note, several old non-scientific calculators had an x^N key for integer powers. The Lloyd's 615 and Sharp EL-8118 [a^N here] are examples.
I have quite a lot of Casios, and the 5000f, too. This small number exponent is a function which, as far as i know, none of the other casios has (at least of the series - neither the 3000, 3600, 3800, 5000f has it). I must also say that i do not really see the need for the function, as x^y is enough for me.
This is intriguing matter.

I'm not a mathematician but I believe the calculator may be using different algorithms depending on the exponent type (integer or real).

Wikipedia has an interesting article here.

However, on my fx-5000F I get exactly the same result using x^n or x^y as long as the exponent is a integer of course.
When the exponent is a real value it is not possible to do any comparison as only the x^y function will accept it.

So in the end I agree that x^y should be sufficient, despite that the x^n is a direct function while the x^y is a shifted function and requires one more keystroke.
If the machine has two different algorithms, it should be able to decide by itself which one to use... I dont know why that was made.
Have you tried both with negative X?
xn does only accept positive integers, no negatives. the main difference to xy, which accepts any numbers, is the designation on the display:

if you type 123 [xy] 456 it shows up on the calc as 123xy456, which calculates 123^456. so, xy is kind of similar to our well-known yx - it raises one number to the power of the second number.

the xn key is more like a shift key. if you want the same result, you have to press 123 [xn] 4 [xn] 5 [xn] 6 (note the second and the third xn). This will be shown on the display as 123456 (with a tiny 4, 5 and 6, but without a special character for the xn key.

This can reduce the memory needed for stored formulas by one byte, and it looks nice - still it is of little use as far as i think.
What about (-1)^2 with either x^n or x^y?
the base number can be any number, just the exponent has to be positive integer. The calculated results are perfectly correct.
here is the relevant part of the manual:
[Image: attachment.php?aid=3042]
Unfortunately you cannot see here that you can repeat the xn structure, that is mentiones somewhere earlier in the manual.
edit: here it is:
[Image: attachment.php?aid=3043]
(01-15-2016 08:08 PM)damaltor Wrote: [ -> ]If the machine has two different algorithms, it should be able to decide by itself which one to use... I dont know why that was made.

It seems to have two algorithms here.This is why the fx-5000F have two different functions from the keyboard: One for real and other for integer values.

In fact there are more key functions available that could be considered redundant as well, if you consider the 10^x or the x^2 keys.
This is not exclusive of this calculator model. Manufacturers like to include direct, some times redundant, access to functions for what they believed were the most popular at the time.

As explained in the link from Wikipedia, x^n is a simple operation of multiplying x n times and can be done with a very simple algorithm, saving power and be faster than other methods.
That is right - but on an old calculator, on which every little firmware byte counts, why would you make two algorithms?

i rather guess that the visual style is why this was made - the calculator is heavily made for formula programming, so seeing 123²³ on the display is somewhat nicer than 123xy23 if you try to recall what this or that formula was made for.
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