exponentiation

Base, exponent and grouping

Record the two operands and preserve grouping rather than inferring it from a flattened string.

1. Which complete expression is the base, and which complete expression is the exponent? definition
2. Do minus signs or nested powers belong inside an operand or outside this exponentiation? boundary

Operator interpretation

Record the notation or language convention that makes the expression an exponentiation.

1. What source or notation convention establishes that the operator denotes exponentiation? provenance
2. How does that convention group an unparenthesised expression such as a^b^c? definition

Operand and result domains

Record the mathematical setting, relevant operations and any permitted extension of the result domain.

1. In which domains or structures are the base, exponent and intended result interpreted? definition
2. May evaluation extend a real-valued expression into complex values, or must it remain within the declared domain? boundary

Power construction

Record whether the power uses repeated multiplication, an inverse, a root-based convention or another specified extension.

1. What is known about the exponent's class, and what definition gives the power meaning for that class? definition
2. For a negative integer exponent, is the base invertible in the selected setting? boundary
3. For a noninteger exponent, which definition or convention authorises the extension beyond integer powers? provenance

Zero and negative-base cases

Record the actual base and exponent conditions before assigning definedness.

1. Can the base be zero, and if so is the exponent positive, zero, negative or still unknown? boundary
2. If both operands are zero, which context-specific convention governs 0^0? definition
3. For a negative real base and a noninteger exponent, does the selected real or complex interpretation define a value? boundary

Selected power values

Record whether an interpretation selects one value or retains multiple values, together with its governing branch convention.

1. Is this power interpreted as single-valued, branch-selected or multivalued? definition
2. If the definition uses a complex logarithm, which logarithm branch or set of logarithm values is used? definition
3. Would crossing a branch boundary require changing the selected value or refusing the proposed continuation? action

Rewrite obligations

Record the intended identity and establish its conditions before using it.

1. Which rewrite is proposed: combining equal bases, distributing a power over a product, or replacing a power of a power? action
2. Are both sides defined and equal under the recorded domain, operand assumptions and branch choices? boundary
3. If the bases belong to a structure with noncommutative multiplication, does the rewrite require a commutativity condition? boundary

Comparison conditions

Record the ordered setting, operand restrictions and direction of monotonicity needed for a comparison.

1. Does the result domain support the requested order comparison? boundary
2. For a positive real base, is it below one, equal to one or above one, and what does that imply when comparing exponents? measurement
3. What bounds on the base and exponent justify a bound on this power without exact evaluation? action

Method and target

Record whether evaluation should produce an exact value, approximation, enclosure or retained symbolic expression.

1. Does the intended use require an exact value, a certified bound or a numerical approximation? action
2. Which evaluation method preserves the declared domain and branch interpretation for these operands? action
3. Would retaining the power symbolically preserve information that the available numerical representation would lose? boundary

Accuracy and range

Record evaluation status, numerical error and representation limits before accepting the result.

1. What precision or error bound accompanies the computed power, and does it meet the intended use? measurement
2. Did evaluation encounter overflow, underflow or a domain error, and does that reflect the mathematics or only the implementation? boundary
3. Would uncertain or rounded operands materially change the result or its definedness, requiring higher precision or an explicit enclosure? action

Kinds and varieties

Reported by the breadth pass; each item needs checking against its source before it becomes normative.

1. Which of these kinds and varieties hold for the sense of exponentiation this model covers, and on what evidence? provenance

Identifiers and schemes

Reported by the breadth pass; each item needs checking against its source before it becomes normative.

1. Which of these identifiers and schemes hold for the sense of exponentiation this model covers, and on what evidence? provenance

Standards and regulation

Reported by the breadth pass; each item needs checking against its source before it becomes normative.

1. Which of these standards and regulation hold for the sense of exponentiation this model covers, and on what evidence? provenance

Real-world use

Reported by the breadth pass; each item needs checking against its source before it becomes normative.

1. Which of these real-world use hold for the sense of exponentiation this model covers, and on what evidence? provenance

Typical measurements

Reported by the breadth pass; each item needs checking against its source before it becomes normative.

1. Which of these typical measurements hold for the sense of exponentiation this model covers, and on what evidence? provenance

Failure modes and hazards

Reported by the breadth pass; each item needs checking against its source before it becomes normative.

1. Which of these failure modes and hazards hold for the sense of exponentiation this model covers, and on what evidence? provenance

Regional variation

Reported by the breadth pass; each item needs checking against its source before it becomes normative.

1. Which of these regional variation hold for the sense of exponentiation this model covers, and on what evidence? provenance

Neighbouring kinds and how to tell them apart

Reported by the breadth pass; each item needs checking against its source before it becomes normative.

1. Which of these neighbouring kinds and how to tell them apart hold for the sense of exponentiation this model covers, and on what evidence? provenance