Can someone please help me with this math problem?

Question

I really have a hard time in my math class, and my profesor explains things very quickly, so either I have to pay attention and not take notes or not takes notes and pay attention. So, it is a catch 22. I just don't want the answer, I would like to know exactly how you go about doing these types of problems.

Here is the problem.... 3a^-2 divided by c^-3

the ^ means to the power of.. how would I solve this step by step, and is there an easier way to do this problem?

Answer 1

3a^-2
-------
c^-3

When you have terms to a negative power, switch the term up or down and change it to positive.

3c^3
------
a^2

So you can switch c^3 to the top and a^2 to the bottom. That's about all you can do unless you had more numbers or terms with similar letters.

Answer 2

All the explanations given are good for how to do this problem. But I have suggestions for how to deal with your hard time in math class. It requires some effort on your part - your professor's not going to change (everyone has their own style and a lot of material to cover, usually) and math is math.
You should have a textbook. If you are in high school and for some reason, they don't give out text books, go to the library and check out a good text book that you find interesting in algebra or whatever the subject you are taking.
Ask the professor for a syllabus - if he has one that has a list of the topics and dates for when he will cover the topics.
At the VERY LEAST, ask him at the end of each class, 'What will we be covering in the next class?'
Then read ahead. Take notes on what will be covered. Understand at least some of it - if not, ask someone who's good in math to help you with the really puzzling pieces. Try to get at least one problem successfully finished.
But then you have to go to class - never miss one. Take notes in class but you will be able to follow a lot better and you may even have a question answered during the class from whatever puzzled you in your reading.
Then do the homework. Check the answers to see if you worked the problem correctly.
Math is built on foundation blocks, one on top of the other. Try to get as many foundation blocks in place as you can.
Your math grade will improve a lot if you do this. Your anxiety level will decrease. Give yourself confidence by taking some practice tests in the book. It takes time - that's just the way studying is.

Answer 3

3a^-2 = 3*a^-2 = 3/a^2 where * is multiplication.

When there is a negative in the exponent, you flip it over.............a^-4=1/a^4

Your problem then becomes:
(3/a^2)/(c^-3), which equals

(3c^3)/ (a^2)

note: it is important to pull your coefficients out before flipping because of negatives in the exponent. Only the number or letter which is raised to the negative becomes the reciprocal.

Answer 4

These types of problems always confuse me. One thing to always note when seeing negative exponents is that it is the same as its reciprocal without the negative. What I mean is:

3a^-2 = 3/a^2

So if you do that both times and then simplify, I'm pretty sure you get something like

[3/a^2] / [1/c^3]
or
3c^3 / a^2

Answer 5

First realize that a^-n = 1/(a^n)

So 3a^-2/c^-3 = 3c^3/a^2, all you are doing is swapping the variables between the numerator and denominator.

Answer 6

3a^-2 divided by c^-3 ... I assume it is 3 * a ^ (-2) ... whenever the power is negetive, you can write that as 1 devided by the same expression in positive .... i.e. 3 / a ^2 .... similarly c ^ -3 is 1/ c^3 ...

hence 3/a^2 divided by 1/c^3 is 3 * (c ^ 3) / (a ^ 2)