We can show this using induction
if x is odd then x + 2 is also odd and x  2 is also odd
Let x = 1. We have (1)^{x} = (1)^{1} = 1
Assume n is odd and (1)^{n} = 1. We shall show (1)^{n+2} = 1
(1)^{n+2} = (1)^{n} * (1)^{2 }= 1 * (1)^{2} = 1 * 1 = 1
Next we shall show (1)^{n2} = 1
(1)^{n2} = (1)^{n} * (1)^{2} = 1 * (1/(1)^{2}) = 1 * (1/1) = 1 * 1 = 1
We can also show this by algebra:
is x is odd x  1 is even
(1)^{x} = 1 * (1)^{x1}
Since x1 is even (1)^{x1} = 1
Then
(1)^{x} = 1 * 1 = 1
Jan 27

Marcus H.