SoP to PoS conversion in the simplest way
start with a karnaugh map:



Then go through your SoPs.  The first is B'C', so you update it as follows:



Then AC:



And finally A'C':



Fill in the rest with 0s:



Next determine the equations for the zeros.  For this 0:



use the (ABC')' = A' + B' + C

For this pair of 0s:



use (A'C)' = A + C'

In order for neither of the zero cases (the singleton or pair) to take affect, multiply the two expressions and get (A+C')(A'+B'+C)