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-1) (2^2)^(k-1) = 6^(k-1) * 4^(2k-2) = 24^(k-1)
So the final answer is:
24^(k-1) / 18
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