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Negative Exponent Calculator — result sheet
Evaluate a nonzero base raised to a negative whole-number exponent and show the reciprocal relationship step by step.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For a nonzero base b and positive whole number n, b^(−n)=1/b^n.
A negative exponent does not make the result negative. It asks for the reciprocal of the corresponding positive power, so the page returns both the positive power and its reciprocal.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Nonzero base — minimum -1000000; maximum 1000000
- Positive exponent n — minimum 1; maximum 1000
Worked example
| Input | Value |
|---|---|
| Nonzero base | 2 |
| Positive exponent n | 3 |
2⁻³ = 1/2³ = 0.125; the positive power is 8.
Assumptions and limits
- The base is finite and nonzero because a zero base cannot be raised to a negative power.
- The displayed exponent is a positive whole number n, so the negative exponent is −n.
- The real-number model is used; no complex branch choices are introduced.
- Very large powers can exceed finite-number precision and are rejected when the result is undefined or non-finite.
- A negative base is allowed because the exponent is an integer.
- The reciprocal identity is an exponent rule, not a statement about changing the sign of the base.
- The output is arithmetic support and does not simplify symbolic variables or algebraic expressions.
- Rounding in the displayed decimal is presentation rounding after the exact rule is applied.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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