Positive exponent
3⁴ = 3 × 3 × 3 × 3 = 81.
Calculate powers of a number
Exponent calculator
Raise a base to an exponent and review the power rules that explain positive, negative, and zero exponents.
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Formula and steps included
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Formula
Exponent and power rules
Exponent: aⁿ = a × a × ... × a using n factors; Negative exponent: a⁻ⁿ = 1 / aⁿ; Zero exponent: a⁰ = 1 when a ≠ 0
An exponent tells how a base participates in repeated multiplication when the exponent is a positive whole number. The base is the repeated factor and the exponent is the number of factors.
Negative exponents represent reciprocals, while a zero exponent produces 1 for every nonzero base. Fractional exponents connect powers with roots and may have domain limits in the real numbers.
How to use the formula
Identify the base and exponent
Keep a negative base grouped so its sign is included in the repeated factor.
Apply the exponent rule
Multiply for a positive whole exponent, use 1 for a zero exponent and nonzero base, or calculate the reciprocal for a negative exponent.
Check domain restrictions
Zero cannot be raised to a negative power, and some negative-base decimal powers do not have real-number results.
Check the scale
Powers can grow or shrink quickly, so confirm the sign and exponent before using the result.
Worked examples
Exponent calculator examples
Negative exponent
2⁻³ = 1 / 2³ = 1/8 = 0.125.
Common questions
Exponent calculator FAQ
What does a negative exponent mean?
A negative exponent takes the reciprocal of the corresponding positive power. For example, 5⁻² = 1/5² = 1/25.
What is zero raised to the zero power?
The expression 0⁰ is indeterminate or defined by convention only in certain contexts. This calculator does not treat it as an ordinary exponent result.
Can an exponent be a fraction or decimal?
Yes, within valid real-number domains. For example, a one-half exponent corresponds to a square root for a nonnegative real base.
Are the base and exponent uploaded?
Your values are not saved by default or uploaded. You can opt into Remember on this device or download a local JSON backup.