Final answer:
To find the quotient and simplify the result of dividing two fractions with variables, we first simplify each fraction and then divide them by each other. The result is (5/3)w^5.
Step-by-step explanation:
First, let's simplify each fraction. The first fraction can be written as (5w10)/(7w6), and the second fraction can be written as (15w4)/(35w5). Simplifying these gives us (5/7)w4 and (3/7)w-1.
Next, divide the two fractions by each other. In division, we subtract the exponents and divide the coefficient terms. So, (5/7)w4 divided by (3/7)w-1 is equal to (5/7)/(3/7) x w4/w-1. This simplifies to (5/3)w5.