Equation 7 · Part 3 · AI Inference Economics in Practice: An Advanced Technical Guide
superscript
superscript
What this part means
A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.
Its job in the formula
A raised mark can be a power or an index. Its position and the surrounding notation determine which.
Full expression→superscript→Article meaning
The passage around this formula
is exceeded. At Anthropic’s five-minute rate, w = 1.25 and 1.28 : the prefix pays for itself starting with the first read after the write, matching the break-even Anthropic’s pricing page states for that duration [ 6 ] . At the one-hour rate, w = 2 and 2.11 , matching the stated two-read break-even for that window [ 6 ] . The formula’s use is computing the same threshold for a w and r that are not round numbers, and deciding, before writing code, whether a prefix’s expected reuse clears the bar for the TTL about to be selected.
Learn the underlying idea
An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.
Open the illustrated exponents: repeated multiplication and powers guide →
Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.