All of the numbers are "calculator words", meaning that rotating 180 degrees makes them look like they're spelling a word. However, they each have one blank at the decimal point which can be filled in with a letter to make an answer to the clue. Here are the clue answers (with the missing letter in brackets) and the rotated numbers:
- BIOLOGIS[T]: One studying living things
- GOGGLE[S]: Swimming accessory
- S[W]OOSH: Nike logo
- B[I]BLE: The Old and New Testaments
- BELIE[F]: Faith
- SLEIGH[T]: ____ of hand (prestidigitation)
- B[R]EEZE: Gentle wind
- L[E]SLIE: Jones of SNL
- I[D]EOLOGIES: Isms
- HELIO[S]: Sun god
- S[O]LEIL: Cirque du ____
- BILLIO[N]S: Showtime TV series
- I[G]LOOS: Homes made of ice
- HOBBI[T]: Halfling
- G[H]IBLI: Totoro studio
- GOOGL[E]: Search engine
- HOBBE[S]: Companion of Calvin
- S[E]USS: Children's author Theodor
- L[E]SBOS: Greek island
- BISHO[P]: Chess piece
- E[L]IGIBLE: Qualified
- GEISH[A]: Japanese hostess
- GOBLI[N]: Small creature of folklore
- B[E]LIZE: Central American country
- S[T]EEL: Alloy of iron and carbon
- GEE[S]E: Birds
- LOS[S]LESS: Like PNG, but not JPEG
- BESI[E]GE: Surround with armed forces
- E[N]GLISH: Spin on a billiards ball
- IGLESI[A]S: Spanish-language singer father or son
- S[T]OOGE: Moe, Larry, and Curly, for example
- H[O]BBIES: Regular pastimes
- BLOGGE[R]: One who writes online
- HILLBILLIE[S]: The Beverly ____, TV show
The missing letters from each group spell out TSWIFTSONG, THESES, PLANETS, and SENATORS. These correspond to the numbers 22, 95, 8, and 100. Plugging those into the final equation yields 22*95*(2^8+1)/100 = 5371.3, which rotates to E?ILES. The only common English word with this pattern is EXILES.