SOLUTION: I am currently working on polynomials and exponents with multiply variables and long division. But on this problem it is set up different and says use the rules of exponents: Divis

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I am currently working on polynomials and exponents with multiply variables and long division. But on this problem it is set up different and says use the rules of exponents: Divis      Log On


   

Question 858007: I am currently working on polynomials and exponents with multiply variables and long division. But on this problem it is set up different and says use the rules of exponents: Division. The problem is 2^-1a^-7b^4 as the denominator and 2ab^-3 as the numerator. If someone could be advise me I would be grateful. I am horrible at math and always have been so please explain in detail. Thanks Shawna
Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
2^-1a^-7b^4 as the denominator and 2ab^-3 as the numerator.

2%5E-1a%5E-7b%5E4%2F2ab%5E-3 .

Look at the rules of exponents which you are learning; read them.
%28b%5E4%29%2F%282%5E1%2Aa%5E7%2A2a%2A%281%2Fb%5E3%29%29
%28b%5E4%29%2F%284a%5E8%2A%281%2Fb%5E3%29%29, combines rules of exponents and commutative property of multiplication and simple multiplication fact
%28%28b%5E4%29%2F%284a%5E8%2A%281%2Fb%5E3%29%29%29%28b%5E3%2Fb%5E3%29, multiplying by 1 to simplify the complex fraction
%28b%5E4%2Ab%5E3%29%2F%284a%5E8%2A1%29
highlight%28%28b%5E7%29%2F%284a%5E8%29%29

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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.
$$$

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.

http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut2_exp.htm