## Intermediate Algebra for College Students (7th Edition)

$0$
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: $=1 + (-1) \\=0$