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Equation 19 · Part 2 · Reliable AI Agents Are Control Systems, Not Chatbots

superscript

qkq^k
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.

The passage around this formula

For a simplified independent model with one-run success probability q , the probability of succeeding in every one of k deployments is qkq^k . At q=0.9 , eight consecutive successes occur with probability only 0.9^8≈\approx0.43 . Independence is again unrealistic, but the calculation expresses the right operational demand: a bank, compiler, or datacenter does not consume an average demo. It consumes a sequence of particular decisions.

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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.

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Sources cited in the article section

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