In general, if Power Artifact is attached to Birthing Pod, Birthing Pod's ability costs either—
"G, T, Sacrifice a creature", or
"1, T, Pay 2 life, Sacrifice a creature".
As you activate Birthing Pod's ability, you determine what (G/P) means, either G or "Pay 2 life", before you figure the total cost to activate that ability (C.R. 601.2b, 601.2f, 602.2b). Thus, the cost to activate Birthing Pod's ability will initially be either—
"1G, T, Sacrifice a creature", or
"1, T, Pay 2 life, Sacrifice a creature",
which is reduced due to Power Artifact by 2, but not in a way that reduces the mana portion of the cost to less than one mana (C.R. 601.2f, 602.2b). This is only possible for the first case, however, so that the 1G portion becomes G, but the 1 portion remains 1 (C.R. 118.7a).
EDIT (Aug. 3): One rule was renumbered with Core Set 2020. Further edited.
You choose wether to pay life or pay mana for a phyrexian mana cost when you choose modes, to pay additional costs etc. very early in the activation process (601.2b as directed by 602.2b). Calculating the actual cost comes later (601.2f as directed by 602.2b). Since you selected to pay life instead of mana, the starting cost includes only 1 which cannot be reduced futher by Power Artifact.
It's very confusing with Phyrexian mana.
Niv-Mizzet Reborn
Feather, the Redeemed
Estrid, the Masked
Teshar
Tymna/Ravos
Najeela, Blade-Blossom
Firesong & Sunspeaker
Zur the Enchanter
Lazav, the Multifarious
Ishai+Reyhan
Click images for decks->
-Prime Speaker Vannifar
---------------------Will & Rowan Kenrith
EDIT (Aug. 3): One rule was renumbered with Core Set 2020. Further edited.
Former Rules Advisor
"Everything's better with pirates." - Lodge
(The Gamers: Dorkness Rising)
"Any sufficiently analyzed magic is indistinguishable from science."
(Girl Genius - Fairy Tale Theater Break - Cinderella, end of volume 8)