Does Ezreal Prodigy work with Death from Below? Do you have to pay the additional power cost?

No, Ezreal, Prodigy does not work with Death from Below.

According to the RiftJudge FAQs (specifically FAQ #8415 and #8509) and the Core Rules (Rule 356.4), Ezreal, Prodigy’s ability only reduces optional additional costs. These costs are specifically identified by having both the text "as an additional cost" and the word "may" (e.g., keywords like Accelerate and Repeat, or specific card text like Blast Corps Cadet).

Here is the breakdown for Death from Below:

• Is it an additional cost? No. The ability on Death from Below is a recursive effect ("You may play this from your trash...") that requires a cost to trigger, but it does not contain the mandatory "as an additional cost" phrasing required to be classified as an optional additional cost that Ezreal can discount.
• Must you pay the power? Yes. Since Death from Below does not meet the specific criteria for Ezreal’s discount, you must pay the full costs as written on the card when playing it.

In summary, because the cost associated with playing Death from Below from the trash is not an "optional additional cost," Ezreal, Prodigy provides no discount for it.