Question

I need to correct my test and I figured out why I missed a few of them but there are some fractions I cannot even understand how to do:

(the exponents are after a carrot and are in parentheses so there is no confusion)

14(2x)^(3)y^(5)
----------------
28x^(7)y^(3)


-3x^(-5)y^(-3)z
----------------
6x^(-3)y^(-5)z^(-2)

Sorry it's looks so confusing...

Answer 1

14(2x)^(3)y^(5)
---------------- =
28x^(7)y^(3)

rewriting:
14(2x)³*y⁵
--------------------------------- =
28x⁷*y³

14*8x³*y⁵
-------------------------------- =
28*x⁷y³

14 into 28 = 2 and 8/2 = 4.

4x³*y⁵
----------------------------- =
x⁷*y³

4*y^5-3
------------------ =
x^7-3

4y²
--------------- =
x⁴

I hope this looks ok and I didn't goof with the superscripts.

Answer 2

One trick that might help you out is to remember that powers subtract when dividing (and add when multiplying) So starting with the original equation, you can pull out all the constants (by putting them to the exponent power) then simply subtract the powers. For instance, the top half of the fraction 14 (2x)^3 * y^5 can be rewritten as 14*2^3 * x^3 * y^5 you can then just subtract the exponents on the bottom of the fraction which gives you (ignoring the constants) x^(-4) * y^(2). All that's left is dealing with the constants (which should be pretty easy) and putting the negative powers on the bottom of the fraction for the final solution.

Best of luck!