Keep in mind the following order of operations rules when raising a negative base to an exponent:
-3^2 (with no parenthesis) means that 3 is being raised to the second power, then multiplied by a negative.
(-3)^2 means that the entire quantity of -3, (i.e., everything inside the parenthesis) is being raised to the second power
-(3)^2 means that 3 is being raised to the second power, then multiplied by a negative. In other words, everything inside the parenthesis is being raised to the second power, then multiplied with whatever is outside of the parenthesis.
These are like the type of problem you are going to see in your early study of exponents. These will be like some of your first homework problems, that's what I meant to say.
Okay simplify -3². Be really careful because it doesn't mean the quantity -3 times itself. What this means is 3² and then negativised. If you want to you might think of this in terms of the order of operations, you need to do the exponent piece before you multiply by -1. So here we go, the exponent piece is going to be 9, 3 times 3 is 9 then I need to negativise my answer, there we go.
This is where I’m going to do the quantity -3 times itself. -3 times -3 is +9. Be really careful with that difference.
This third part is a little bit tricky. I know I’m going to be doing my exponent piece first just like I did here my exponent part first and then negativise my answer. So I’m going to have to do 2 times itself on top of 5 times itself and then don't forget that negative sign at the end. These problems can be really quick, which is a good thing because you can do your homework quickly.
The bad part of it is, it’s easy to bang right through without thinking about what you’re doing. Like a lot of times this is the kind of homework that my students get the lowest scores on because they think they can do it just like this but they make little funny mistakes with the negative signs. So when you come to these home work problems make sure you're being careful if the negative is outside the parenthesis verses inside. If it's inside you are going to be squaring that negative quantity if it's outside you are going to be squaring the base first and then negativising your answer like in part A and also part C.