Answer
$1$
Work Step by Step
RECALL:
(1) $a^{mn} = (a^m)^n$
(2) $i^2=-1$
(3) $a^{m+n} = a^m \cdot a^n$
Use rule (1) above to obtain:
$=(i^2)^{100}$
Use rule (2) to obtain:
$=(-1)^{100}$
Note that when $-1$ raised to an even power, the result is $1$.
Thus,
$(-1)^{100} = 1$
