negative power of number inside parenthesize My algebra textbook and calculator says
$$(-3)^0=1 \quad \& \quad -3^0=-1$$
Why does the paranthesis make a difference on the negative/positive of the result?
 A: When parentheses are present, it's clear how to do things; but with parentheses missing, there can be multiple interpretations, and we have to pick one by convention. 

Let's say you want to evaluate the expression "$4-3+1$". There are two reasonable things you could do:


*

*First do "$4-3$," which gives $1$; then add $1$, giving $2$. That is, read the problem as $$(4-3)+1.$$

*First do $3+1$, giving $4$, and then subtract that from $4$, giving $0$. That is, read the problem as $$4-(3+1).$$
Although sometimes parentheses aren't needed, in general they are.
This is exactly what's going on here! The expression "$-3^0$" could be interpreted as:


*

*$(-3)^0$


or 


*

*$-(3^0)$.


If we had parentheses, we'd know which it was easily. 
In lieu of parentheses, we just fix some convention of which operations to do first - that is, what our order of operations is. There isn't necessarily a good argument for what we choose here, we just need to choose something and stick with it.
As it happens, the convention is that exponentiation binds more tightly than multiplication ($-3$ is just $(-1)\cdot 3$), so we read "$-3^0$" as "$-(3^0)$." But the convention could have gone the other way.
