Exponent Calculator
Compute powers and exponents, including negative and fractional exponents.
Enter a base and an exponent to compute baseexponent. Both fields accept decimals and negative numbers.
What is an Exponent?
An exponent indicates how many times a number, called the base, is multiplied by itself. In the expression bn, b is the base and n is the exponent (or power). For example, 25 means 2 × 2 × 2 × 2 × 2 = 32.
Laws of Exponents
- Product rule: bm × bn = bm+n
- Quotient rule: bm ÷ bn = bm−n
- Power of a power: (bm)n = bm×n
- Power of a product: (a × b)n = an × bn
- Zero exponent: b0 = 1 (for b ≠0)
Negative and Fractional Exponents
A negative exponent represents the reciprocal of the base raised to the positive exponent: b−n = 1 / bn. For example, 2−3 = 1 / 23 = 1 / 8 = 0.125.
A fractional exponent represents a root. The expression b1/n equals the n-th root of b, and bm/n equals the n-th root of bm. For example, 91/2 = √9 = 3 and 82/3 = (∛8)2 = 4.
Note: A negative base with a fractional exponent (such as (−8)1/2) often has no real-number result and is undefined in the real numbers (the result would be a complex number). This calculator reports such cases as undefined.
Related Calculators
Note: This calculator computes powers and exponents using standard floating-point arithmetic. Very large or very small results are shown in scientific notation and may be subject to rounding. While we strive for accuracy, please verify important calculations independently. This tool is for educational and informational purposes.