Question 858007
It's easier to show this on a piece of paper, so check out the following sheet of paper:
step 1 shows you the problem as i interpreted it.
step 2 shows you the solution.
step 3 shows you how i got 4 from 2 / 2^-1.
step 4 shows you how i got a^8 from a / a^-7.
step 5 shows you how i got 1 / b^7 from b^-3 / b^4.
<img src = "http://theo.x10hosting.com/2014/mar291.jpg" alt="$$$" </>


the basic principles of exponent arithmetic that were used in this problem are:


x^a * x^b = x^(a*b)
x^a / x^b = x^(a-b)
x^-a = 1/x^a


other principles that can be used for other problems are:


1/x^-a = x^a
(x^a)^b = x^(a*b)
(x^a*y^b)^c = x^ac*y^bc


here's a good tutorial that explains all of that with examples and a small number of exercises that you can use to test yourself.


<a href = "http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut2_exp.htm" target = "_blank">http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut2_exp.htm</a>