Answer
$-1$
Work Step by Step
Note that
$(-i) = -1(i)$
Thus, the given expression is equivalent to:
$=[-1(i)]^6$
Use the rule $(ab)^m = a^mb^m$ to obtain:
$=(-1)^6(i)^6
\\=1(i^6)
\\=i^6$
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:
$i^{6}=(i^2)^{3}$
Use rule (2) above to obtain:
$=(-1)^{3}
\\=(-1)(-1)(-1)
\\=-1$
