Exponent Calculator

What this exponent calculator does

An exponent tells you how many times to multiply a base by itself. This calculator evaluates a base raised to a power, including negative exponents and fractional exponents.

For example, 2^5 means 2 × 2 × 2 × 2 × 2 = 32.

How to use this calculator

1. Enter the base.
2. Enter the exponent.
3. Click Calculate.

The default example is 2^5.

Exponent rules

a^m × a^n = a^(m+n)
a^m ÷ a^n = a^(m−n)
(a^m)^n = a^(m×n)
a^−n = 1 / a^n
a^(1/n) = the nth root of a
a^0 = 1  (for a ≠ 0)

A negative exponent means reciprocal. A fractional exponent such as 1/2 means a square root, and 1/3 means a cube root.

What the results mean

The result is the value of the base raised to the exponent. For 2^5, the result is 32.

If the result is very large, it may be shown in scientific notation or rejected as too large for reliable display.

Assumptions and limitations

Zero to a negative power is undefined. Negative bases with fractional exponents may produce complex results, which this calculator does not display. Very large exponents can exceed the precision of standard floating-point arithmetic.

The calculator is for real-number arithmetic, not symbolic algebra.

Frequently asked questions

What does a negative exponent mean?

It means the reciprocal of the positive power: 2^−3 = 1/2^3 = 0.125.

What does a fractional exponent mean?

The denominator is the root. For example, 9^(1/2) = 3 and 8^(1/3) = 2.

What is anything to the power of zero?

Any nonzero number to the power zero is 1. Zero to the zero power is usually treated as indeterminate in algebra.

Why is my result rounded?

The calculator uses standard floating-point arithmetic. For exact integer powers, the displayed value is usually exact; very large or fractional results may be rounded.

Source

Reference: Wolfram MathWorld — Exponent.

Disclaimer

This calculator is for educational purposes. Verify exact or high-precision results with an appropriate math tool.