SOLUTION: Simplify the expression. Express your answer so that only positive. (4x^-1y^1/3)^3/2 divided by (xy)^3/2

Algebra ->  Exponents -> SOLUTION: Simplify the expression. Express your answer so that only positive. (4x^-1y^1/3)^3/2 divided by (xy)^3/2       Log On


   

Question 716671: Simplify the expression. Express your answer so that only positive.
(4x^-1y^1/3)^3/2 divided by (xy)^3/2


Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%284x%5E%28-1%29y%5E%281%2F3%29%29%5E%283%2F2%29%2F%28xy%29%5E%283%2F2%29
Using the rule:
a%2Ab%29%5En+=+a%5En%2Ab%5En
in both the numerator and denominator we get:


Next we'll use the power of a power rule in the numerator:

Next we'll simplify 4%5E%283%2F2%29 using the rule a%5E%28m%2Fn%29+=+%28root%28n%2C+a%29%29%5Em:
4%5E%283%2F2%29+=+%28root%282%2C+4%29%29%5E3+=+2%5E3+=+8
Now our expression is:

Now we'll use the a%5Em%2Fa%5En+=+a%5E%28%28m-n%29%29 rule to divide the x's and y's:
8%2A%28x%5E%28%28-3%2F2%29-%283%2F2%29%29%29%2A%28y%5E%28%281%2F2%29-%283%2F2%29%29%29
Subtracting the fractions:
8%2A%28x%5E%28%28-6%2F2%29%29%29%2A%28y%5E%28%28-2%2F2%29%29%29
which simplify to:
8%2A%28x%5E%28%28-3%29%29%29%2A%28y%5E%28%28-1%29%29%29
This is a simplified expression. Assuming that the "only positive" in your post means "using only positive exponents" then we have a little more work to do. Using the rule a%5E%28%28-n%29%29+=+1%2Fa%5En we get:
8%2A%281%2Fx%5E3%29%2A%281%2Fy%5E1%29
which simplifies to:
8%2F%28x%5E3%2Ay%29