We can simplify the expression in the numerator first.
4(k^2)^4 = 4(k^(2*4)) = 4(k^8)
Now we can substitute this into the original expression:
4(k^2)^4/12k^7 = 4(k^8)/12k^7
Simplifying further, we can cancel out a factor of 4 and simplify the denominator:
4(k^8)/12k^7 = (k^8)/(3k^7)
Finally, we can simplify the expression by subtracting the exponents:
(k^8)/(3k^7) = k^(8-7)/(3) = k/3
Therefore, the simplified form of the expression 4(k^2)^4/12k^7 is k/3.