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THE NOTATION DESK / 03 · ARITHMETIC

Exponent Calculator

Raise an exact decimal base to an integer power. See why negative powers use reciprocals, how parity controls the sign, and when a decimal answer must be rounded.

Free · No sign-up · Instant, browser-only results

Set out your numbers

Use numbers and non-identifying study notes only. No names, account data or private records are needed.

Decimal or e notation, e.g. -0.00450 or 4.50e-3. No commas, fractions, units or expressions. Up to 300 coefficient digits; e exponent −1000 to 1000.
Whole numbers from -1000 to 1000.
Whole numbers from 1 to 30.
Optional; maximum 180 characters. Displayed literally and excluded from the arithmetic.

No calculation API or saved history. Inputs stay in the current working page.

THE NOTATION DESK / YOUR WORKING NOTE

The working belongs beside the answer.

Enter your values, then show the result and its steps here. Download and print controls appear after a valid calculation.

Study support, not a substitute for a teacher or textbook. Check input conventions, exactness and any labelled rounding before using or sharing an answer.

Behind the result - No mystery in the method

The entire base is treated as parenthesized: entering −2 and power 2 means (−2)^2, not −(2^2). Positive integer powers multiply numerator and denominator separately; negative powers invert the result. Nonzero bases to power zero return 1. The tool rejects 0^0, zero to a negative power, non-integer exponents and powers beyond its 6000-digit work estimate. Exact rational results are retained. Terminating decimals are expanded exactly; repeating decimals are labelled and rounded for scientific display with the chosen significant figures, half away from zero.

This tool does not store inputs, fetch live data or replace a teacher or textbook explanation. Blank optional fields are omitted. Text is displayed literally, not interpreted as HTML.

Changing an input clears the old answer so it cannot be mistaken for the new calculation. Download text makes a local copy of the current working. Print / Save PDF uses the browser’s print controls. Review any note before sharing.

Before you go

Why is (−2)^2 positive?

Multiplying two negative factors gives a positive result. An odd integer power of a negative base stays negative; an even integer power is positive. This form always parenthesizes the whole entered base, so it differs from an unparenthesized −2^2 expression.

Can I calculate square roots or fractional powers?

Not with this tool. It accepts integer exponents from −1000 to 1000, subject to a work-size limit. Fractional or complex powers require domain and branch choices that this calculator deliberately does not guess.

What happens at zero and negative powers?

A negative exponent means taking a reciprocal, so a zero base is invalid there. This tool also leaves 0^0 undefined. For a nonzero base, power zero is exactly 1.

Why can a valid power be refused?

The tool estimates the size of integer work before exponentiation and rejects inputs over a 6000-digit bound. Expanded decimals also have a 6500-place display limit. These limits protect browser responsiveness; they are not mathematical restrictions on exponentiation.

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