Answer to Question #193118 in Algebra for Desmond

Question

Prove that any even power of a Nonzero integer is positive. That is, if X does not equal to zero in integers, then X²ⁿ is positive for every positive integer n.

Answer 1

$x \neq 0, x^2>0$ because

$\ if\ x>0, x^2=x*x>0,\\if\ x<0, x^2=x*x=(-x)*(-x)>0$

$x^{2n}=(x^2)^n>0$

since raising a positive number to a power keeps it positive