To simplify the expression:

24^(k-1) / 18 4^(k-1) 6^(k-4)

First, we can rewrite 24 as 6 4 and 18 as 6 3:

(64)^(k-1) / (63) 4^(k-1) 6^(k-4)

Now we can distribute the exponents:

6^(k-1) 4^(k-1) / (63) 4^(k-1) 6^(k-4)

Now combine like terms:

6^(k-1) 4^(k-1) 4^(k-1) 6^(k-4) / (63)

Add the exponents for the 4 terms:

6^(k-1) 4^(2k-2) 6^(k-4) / (6*3)

Now we can combine the like terms in the numerator:

6^(k-1) 4^(2k-2) 6^(k-4) / 18

Now simplify the expression:

6^(k-1) 4^(2k-2) 6^(k-4) / 18

6^(k-1) 4^(2k-2) = 6^(k-1) (2^2)^(k-1) = 6^(k-1) * 4^(2k-2) = 24^(k-1)

So the final answer is:

24^(k-1) / 18