# Exponent / Power Calculator

Calculate any number raised to any power. Supports positive, negative, and fractional exponents. Free online exponent calculator with step-by-step results.

## What this calculates

Calculate the result of raising any base number to any exponent with this free online tool. It handles positive, negative, and fractional exponents, and displays the reciprocal of the result for quick reference.

## Inputs

- **Base** — The number to be raised to a power.
- **Exponent** — The power to raise the base to. Can be positive, negative, or fractional.

## Outputs

- **Result** — The value of base raised to the exponent.
- **Expression** — formatted as text — The mathematical expression evaluated.
- **Reciprocal (1/result)** — The reciprocal of the result.

## Details

Exponentiation is one of the fundamental operations in mathematics. When you raise a base number b to a power n, written as b^n, you multiply b by itself n times.

Key Rules of Exponents

- Positive exponent: b^n = b x b x b x ... (n times). For example, 2^5 = 2 x 2 x 2 x 2 x 2 = 32.

- Zero exponent: Any non-zero number raised to the power of 0 equals 1. For example, 7^0 = 1.

- Negative exponent: b^(-n) = 1/(b^n). For example, 2^(-3) = 1/8 = 0.125.

- Fractional exponent: b^(1/n) = the nth root of b. For example, 8^(1/3) = cube root of 8 = 2. More generally, b^(m/n) = (nth root of b)^m.

- Product rule: b^m x b^n = b^(m+n).

- Power rule: (b^m)^n = b^(m x n).

Exponents are used extensively in science (scientific notation), finance (compound interest), computer science (binary systems), and physics (exponential growth and decay).

## Frequently Asked Questions

**Q: What does raising a number to a power mean?**

A: Raising a number (the base) to a power (the exponent) means multiplying the base by itself a specified number of times. For example, 3^4 means 3 x 3 x 3 x 3 = 81. The base is 3 and the exponent is 4.

**Q: Why is any number raised to the power of 0 equal to 1?**

A: This follows from the rule that b^m / b^m = b^(m-m) = b^0. Since any non-zero number divided by itself is 1, b^0 must equal 1. This convention keeps the laws of exponents consistent.

**Q: How do negative exponents work?**

A: A negative exponent means you take the reciprocal of the base raised to the positive version of the exponent. For example, 5^(-2) = 1/(5^2) = 1/25 = 0.04. Negative exponents do not make the result negative.

**Q: What are fractional exponents?**

A: A fractional exponent like b^(m/n) means take the nth root of b and raise it to the power m. For example, 27^(2/3) = (cube root of 27)^2 = 3^2 = 9. The denominator is the root, and the numerator is the power.

**Q: What is 0 raised to the power of 0?**

A: The expression 0^0 is mathematically debated, but by convention it is defined as 1 in most contexts (combinatorics, set theory, computer science). This convention simplifies many formulas, such as the binomial theorem and Taylor series.

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Source: https://vastcalc.com/calculators/math/exponent
Category: Math
Last updated: 2026-04-21