compound fractions lowest terms?

Question

20t^3u
----------
7rs^2
-----------
5t^4u^2
-----------
28s^5

Starting from the bottom up,
and then I get into a quandry..

Answer 1

(20t^3u/5t^4u^2)(28s^5/7rs^2)
=4/tu*4s^3/r
=16s^3/rtu

Answer 2

Without parentheses, it looks like this equals (20t^3u)/(7rs^2*5t^4u^2*28s^5) which equals (2/7)*t^2/(rs^7u).

But "starting from the bottom up," let a=20t^3u, b=7rs^2, c=5t^4u^2, d=28s^5. Then your fraction becomes a/b/c/d,
or with parentheses a/(b/(c/d)) = a/(b*(d/c)) = a/((bd)/c) =
a*(c/(bd)) = (a*c)/(b*d) = (20t^3u*5t^4u^2)/(7rs^2*28s^5) =
(100t^7u^3)/(196rs^7).

However most likely (because 7 divides 28 evenly and 5 divides 20 evenly), your fraction is (a/b)/(c/d) =(a/b)*(d/c) = (a*d)/(b*c) =
(20t^3u*28s^5)/(7rs^2*5t^4u^2) = (16s^3)/(rtu). This would be most likely also if the middle line is the longest of the three fraction bars.

Aren't fractions fun?