Exponent Calculator

Calculate a number raised to a power with this free exponent calculator. Enter positive, negative, zero, decimal, or fractional exponents and get the result with a clear mathematical explanation.

Calculate a Power

For the expression aⁿ, enter the base a and exponent n.

What Is an Exponent?

An exponent indicates how many times a base is used as a factor for positive whole-number exponents. In aⁿ, a is the base and n is the exponent.

Example: 2⁴ = 2 × 2 × 2 × 2 = 16

Exponents are widely used in algebra, geometry, science, engineering, compound growth, and scientific notation.

Exponent Rules

Zero exponent

a⁰ = 1, when a ≠ 0

Any nonzero number raised to zero equals one.

Negative exponent

a^-n = 1 / aⁿ

A negative exponent means take the reciprocal.

Multiplication

a^m × aⁿ = a^m+n

Add exponents when multiplying powers with the same base.

Division

a^m / aⁿ = a^m-n

For a nonzero base, subtract exponents when dividing powers with the same base.

Power of a power

(a^m)ⁿ = a^mn

Multiply the exponents.

Fractional exponent

a^p/q = (q-th root of a)^p

The denominator gives the root and the numerator gives the power.

Worked Examples

Expression	Calculation	Answer
3⁴	3 × 3 × 3 × 3	81
2^-3	1 / (2 × 2 × 2)	0.125
7⁰	Nonzero number to the zero power	1
16^1/2	Square root of 16	4
8^2/3	Cube root of 8, squared	4
(-8)^1/3	Real cube root of -8	-2

Frequently Asked Questions

How do I calculate a number raised to a power?

Enter the base and exponent and click Calculate Exponent. For example, a base of 2 and an exponent of 5 produce 32.

Can I use negative exponents?

Yes. A negative exponent gives the reciprocal of the corresponding positive power, provided the base is nonzero.

Can I enter fractions as exponents?

Yes. Enter a fraction such as 2/3. For negative bases, the calculator checks whether the fraction gives a real result.

Why is zero raised to a negative exponent undefined?

A negative exponent requires taking a reciprocal. For zero, that would involve division by zero, which is undefined.

What is scientific notation?

Scientific notation expresses a number as a value multiplied by a power of ten. It is useful for very large and very small numbers.