What is the simplified value of the sum: $-1^{2004} + (-1)^{2005} + 1^{2006} -1^{2007}$?
Ok so the first term is $-1^{2004}$. So the first term is just $-1$. Since the base is $-1$, it remains $-1$ raised to any odd integer power. That's correct. So $(-1)^{2005} = -1$. The third term is $1^{2006}$. Since the base is $1$, it remains $1$ raised to any integer power. That's correct. So $1^{2006} = 1$. The fourth term is $-1^{2007}$. That's correct. So $-1^{2007} = -1$. And now we can add up all the terms: $-1 + (-1) + 1 -1$ which is $-2$. That's correct. So $-1^{2004} + (-1)^{2005} + 1^{2006} -1^{2007} = -2$.

