Education / Algebra
Exponent Calculator: Exact Powers, Fractions and Scientific Notation
Calculate a raised to b, including fractional and negative exponents. See exact results for integer powers, approximate scientific notation and the calculation steps.
Exponent Calculator: Exact Powers, Fractions and Scientific Notation: An integer base and integer exponent produce an exact integer, or an exact reciprocal for a negative exponent. Other real powers are approximate. Reduced fractions with odd denominators allow real roots of negative bases. Zero to zero or a negative power is treated as undefined. Exact output is limited to 10,000 digits. Runs 100% locally in your browser with zero server file uploads.
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Enter exponents as integers, decimals or fractions such as 1/3. Negative powers give reciprocals.
2 raised to 10
Exact integer or fraction1024
- Read the base a = 2 and exponent b = 10.
- Multiply powers by repeated squaring; an odd remaining exponent multiplies the accumulator.
Show exact multiplication steps
| Remaining exponent after halving | Accumulator |
|---|---|
| 5 | 1 |
| 2 | 4 |
| 1 | 4 |
| 0 | 1024 |
Integer bases and integer powers use exact arithmetic, up to 10,000 result digits. Other results use approximate real arithmetic.
Exponent rules
OpenStax describes integer exponent rules (https://openstax.org/books/intermediate-algebra-2e/pages/1-2-exponents-and-scientific-notation). A negative exponent takes a reciprocal and a non-zero base to power zero equals one.
Rational exponents and exact arithmetic
OpenStax covers roots and rational exponents (https://openstax.org/books/intermediate-algebra-2e/pages/8-1-simplify-expressions-with-roots). ECMAScript defines arbitrary-precision integers (https://tc39.es/ecma262/#sec-bigint-objects). The exact output follows integer multiplication rather than rounded floating-point multiplication.
How to use it
- Enter a decimal or integer base.
- Enter an integer, decimal or fraction exponent such as 1/3.
- Read the exact result when available, scientific notation and multiplication steps.
Privacy & limitations
Your inputs and files are processed in your browser. Nothing is uploaded.
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Frequently asked questions
What does a negative exponent mean?
It means the reciprocal: 2^−3 = 1/2^3 = 1/8. It does not make a positive base negative.
Can I take a fractional power of a negative number?
Yes, when the fraction has an odd denominator after reduction. For example, (−8)^(1/3) = −2 and (−8)^(2/3) = 4. Enter the fraction explicitly; a rounded decimal does not identify the same rational power.
Why is there an exact result and an approximate result?
Integer arithmetic can retain every digit. Fractional powers and scientific notation use approximate arithmetic, so their last displayed digits can differ from the exact decimal expansion.
Can the answer exceed the usual numeric range?
Integer powers can produce exact output up to 10,000 digits. Scientific notation can describe magnitudes beyond ordinary decimal numeric output, including very small reciprocals.
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