I looked through that test and it looks like the first few questions deal with reducing fractions and simplifying terms. The point of it is to be able to write a long equation in as little space as possible. For example, I can write out a*a*a*a*a*a*a. However, I can also make it easier for myself by instead writing a^7 where ^ indicates that the next number is an exponent. Same goes for addition. That is, I can write a+a+a+a+a, but you should know that this is the same as 5*a, or 5a. Obviously, the 2nd way of writing stuff takes muuuch less space.
Another thing you need to know is negative exponents. Exponent is the small number on the upper right. Since d2jsp doesn't have included ways of writing it the way you will see it on the paper, I will use the ^ symbol. That means 5^2 = five squared, or five to the second power. You should know that if you have a term a^b that means that you are multiplying the term a by itself b amount of times. Sometimes you get negative exponents. That means that you are actually taking an exponent of the reciprocal of the term. Reciprocal means that if you have a fraction x/y, its reciprocal = y/x. So let's say you have (x/y)^(-5). This is the same as (y/x)^5.
So in question 1, you are faced with a*b^3*c^2*[(2a^2*b)/(c^4)]^(-1). First thing to do would be flip the fraction in order to get rid of the negative exponent. So
a*b^3*c^2*[(2a^2*b)/(c^4)]^(-1) = a*b^3*c^2*[(c^4)/(2a^2*b)]^(1), and since anything raised to the first power is just the term by itself, this equals a*b^3*c^2*[(c^4)/(2a^2*b)]. In multiplication, order doesn't matter. That's why a*b = b*a. Also, (a*b)*c = a*(b*c), that's why you can rewrite the term as [(a*b^3*c^2*c^4)/(2a^2*b)]. You notice that that you have two terms that have c in them right next to each other. What we're gonna do next is called combining like terms. c^2 and c^4 both have cs in them, so you can combine them together. They have different powers though, however, as I mentioned earlier, powers just mean multiplying the same term a certain amount of time. For the first c, we multiply it together twice, then we have the second term, in which we multiply the second c 4 times. So in total, you have (c*c)*(c*c*c*c) and this is the same as c^6. From this you should remember that if you ever have something that looks like a^x*a^y = a^(x+y). Going back to problem number 1, you get [(a*b^3*c^6)/(2a^2*b)]. Now let's look for more like terms. There's a at the top and bottom of the fraction, so you can cancel one of them out from both top and bottom (you should know that a/a = 1, and x*1 = x, which is why we are allowed to do that), so cancelling one of a's on both bottom and top gives us: [(b^3*c^6)/(2a*b)]. Notice that the 2 in front of a stays there, but instead we take the exponent. That's because that 2 is multiplied by a*a. We want to take out the actual a, not whatever a is being multiplied by. The only term left that repeats itself in here is b, so we do the same thing, that is, cancel it out. We get: [(b^2*c^6)/(2a)]. All the terms in here are now different, and so we can't reduce it anymore. Our answer looks just like d.
2. We start off with
(t+3)(2t-1) - 3(t+2)
They ask us to multiply it out, so let's follow directions. Now, i don't know if you heard this before, but there's a process for multiplying things that look like (a+b)(c+d) and it's called FOIL. The idea is that you start by multiplying First terms in both parentheses: a*b, then the Outside terms a*d, then the Inside terms b*d, then the Last terms, b*d. So let's do that in the question: t*2t+t*(-1)+3*2t+3*(-1) -3(t+2). Now we take care of those last terms, by multiplying the 3 out. So we get: t*2t+t*(-1)+3*2t+3*(-1) -3t + (-3)*2. Now let's simplify just a bit: 2t^2 - t+6t - 3 -3t -6. Now, we are going to once again combine like terms, but keep in mind that in addition, a and a^2 are not like terms. They have to have the same power. So we group them all together first: 2t^2 + (6t-3t-t) + (-3 - 6) and actually combine the like terms: 2t^2+2t -9. That looks just like b!
Let me know if I'm clear enough or if there's any parts you'd like me to explain in more depth or any details you don't seem to fully understand or if I'm writing too much details :P. I'll be happy to explain the rest of the questions once I get a reply from you on how you understand those two if you want. You can also pm me and maybe I could explain it better over skype or something.