Answer
$0$
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:
$=(i^2)^{14}+(i^2)^{15}$
Use rule (2) above to obtain:
$\\=(-1)^{14}+(-1)^{15}$
Note that:
(a) When $-1$ is raised to an even power, the result is $1$.
(b) When $-1$ is raised to an odd power, the result is $-1$
Thus, the expression above simplifies to:
$=1 + (-1)
\\=0$
