To simplify this expression, we will use the rules of dividing fractions:

First, simplify each fraction:

(7p^4/10q^3) = 7p^4 / 10q^3(5q/14p^2) = 5q / 14p^2(3p/4q^4) = 3p / 4q^4

Now simplify the entire expression:

(7p^4 / 10q^3) / (5q / 14p^2) / (3p / 4q^4)
= (7p^4 / 10q^3) (14p^2 / 5q) (4q^4 / 3p) (Flip the second and third fractions and multiply instead of divide)

= (98p^6 p 4q^4) / (10q^3 5q 3)
= (392p^7q^4) / (150q^4)

= 392p^7q^4 / 150q^4
= 196p^7 / 75

So, the simplified expression is 196p^7 / 75.