If a/b = 3/4, b/c = 4/3 and c/d = 5/6, then the sum of the numerator and the denominator (which are coprimes) of (a/d)¹⁰ is:

a:b:c:d = 3:4:3:... Working out a/d: a/d = (a/b)×(b/c)×(c/d) = (3/4)×(4/3)×(5/6) = 5/6... Let's recalculate: a/b=3/4, b/c=4/3→c=3b/4=3(4a/3)/4=a, c/d=5/6→d=6c/5=6a/5. So a/d=5/6. (a/d)¹⁰=(1/2)¹⁰=1/1024. Sum=1+1024=1025.