how does A'B'C' convert to A'+B'+C'?
\$\bar A \bar B \bar C \$ does not equal  \$  \bar A+ \bar B + \bar C \$

If you let A=0, B= 1, and C=1

Then \$\bar A \bar B \bar C \$ = 0 and \$  \bar A+ \bar B + \bar C \$ = 1

It's clear that they are not the same

If you apply deMorgan's for \$\bar A \bar B \bar C \$ you would end up with  (A+B+C)'. Which is what you said.