Powers, reciprocals, and fractional exponents
The power is the numeric value of the expression. A negative exponent produces a reciprocal, while a fractional exponent on a positive base represents a root followed by a power.
For an integer-degree radical, including an odd root of a negative number, use the Root Calculator .
The formula
The calculation uses the browser’s real-number exponentiation operation. Integer exponents retain the sign rule for negative bases. This tool excludes 0⁰ and zero raised to a negative exponent because their interpretation requires a different convention or division by zero.
Worked example
For base 2 and exponent 10, the result is 1,024 and its reciprocal is 0.0009765625. Changing the exponent to −3 gives 0.125, because 2⁻³ = 1/8.
How to use this calculator
- Enter the number being raised to a power.
- Enter its exponent; use a minus sign for a reciprocal power.
- Calculate and check whether the result needs scientific notation.
A minus sign and parentheses change the expression
Here, the entire base is raised to the exponent. Entering base −3 and exponent 2 calculates (−3)² = 9. It does not calculate −(3²) = −9. This distinction matters when checking expressions copied from a worksheet or a spreadsheet, where operator precedence may differ.
Fractional exponents and real roots
For a positive base, an exponent of 0.5 means the principal square root. An exponent of 1/3 is entered as a decimal approximation, so it need not yield an exact cube root. Use the root calculator for an integer root degree, particularly for odd roots of negative numbers, which this power form deliberately does not parse.
Large and small powers
Powers can grow beyond the largest finite number or shrink below the smallest positive number representable by JavaScript. The calculator reports those conditions instead of displaying infinity or silently treating a positive quantity as zero. Displayed decimals are rounded; they are unsuitable for exact symbolic proofs or very large integer arithmetic.
Assumptions & limitations
What this calculation assumes
- Only finite real-valued results are returned.
What to keep in mind
- No complex powers, fraction-expression parser, or arbitrary-precision integer output.
Common questions
Why can’t I use a fractional exponent with a negative base?
A decimal exponent does not specify an exact rational denominator. Use an odd integer degree in the root calculator to find a real root of a negative number.
What is any nonzero number to the zero power?
It is 1. Zero to the zero power is excluded here rather than choosing a context-dependent convention.