Answer
This statement is true for some integers and false for others.
Work Step by Step
Taking $a=2$ and $n=3$, we get $-a^{n}=-2^{3}$$=-(2\cdot2\cdot2)=-8=(-2)\cdot(-2)\cdot(-2)=(-2)^{3}$, which shows that the statement holds for at least some integers.
However, taking $a=2$ and $n=2$, we get $-2^{2}=-(2\cdot2)$$=-4$, but $(-2)^{2}=(-2)\cdot(-2)=+4$. Hence, the statement holds for some integers but not for others.
In fact, the statement is true for integers if and only if $n$ is odd.
