Answer
$1$
Work Step by Step
Note that
$(-i) = -1(i)$
Thus, the given expression is equivalent to:
$=[-1(i)]^4$
Use the rule $(ab)^m = a^mb^m$ to obtain:
$=(-1)^4(i)^4
\\=1(i^4)
\\=i^4$
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:
$i^{4}=(i^2)^{2}$
Use rule (2) above to obtain:
$=(-1)^{2}
\\=(-1)(-1)
\\=1$
