# Negative Numbers to the power of 0

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Simon Hunter on 18 Nov 2020
Commented: TADA on 19 Nov 2020
Hi All,
New-again matlab user after a decade away; having trouble with raising a negative number to the power 0.
I recognise that:
• (-2)^0 = 1 and
• -2^0 = -1.
In my code, I am trying to populate a 5x5, row by row filling the columns with elements of one 1x5 row vector to the power of another 1x5 vector.
I have written a very basic, and probably inefficient way of doing this with two for loops, but when it comes to raising a negative number to the power 0 and storing it, I get 1 as opposed to what I think is correct; -1.
I presume Im missing something very basic but would really appreciate any help; Thank you!
k = [0:4]
x = [-2.0 3.0 9.0 2.0 25.0]
A = ones(5,5);
for row = 1:length(k)
for col = 1:length(k)
A(row,col) = x(col)^k(row);
end
end
This is what I get: But I think the top left should be -1 since -2^0 = -1
1 1 1 1 1
-2 3 9 2 25
4 9 81 4 625
-8 27 729 8 15625
16 81 6561 16 390625
Bruno Luong on 18 Nov 2020
What a mess.

Ameer Hamza on 18 Nov 2020
Edited: Ameer Hamza on 18 Nov 2020
You can do it without for-loop
k = 0:4;
x = [-2.0 3.0 9.0 2.0 25.0];
A = x.^(k.')
Also, x(col)^k(row) is equivalent to (-2)^0, not -2^0.
For example, what you you expect the output of following code to be
x = -2;
y = x^2
should y be 4 or -4?
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Simon Hunter on 18 Nov 2020
Thank you!

### More Answers (1)

TADA on 18 Nov 2020
Edited: TADA on 18 Nov 2020
Any arithmetic operation performed on variables will treat the variables as if it was wrapped with parentheses.
Try this simple example:
x = -2;
y = x^0
y = 1
In my opinion, this is the correct result, which takes into account the proper order of operations, but if you really want that to keep the original sign, you can multiply your result by the sign of the original number:
y = sign(x) * x^0
y = -1
TADA on 19 Nov 2020
Good point