Exponent & Power Calculator

Calculate powers, negative exponents, fractional exponents, and nth roots with clear steps and real-number domain checks.

Powers Fractional Exponents Nth Roots
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Calculation type

Real-number calculator

Negative bases work with integer powers and fractions that have odd denominators.

Base and exponent

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Output

Preview

Quick load:

Calculating power...

Enter a base and exponent to see the result

The result will show the decimal answer, scientific notation, steps, and a magnitude chart.

Example: 2^10 = 1024 2 10 1024 base exponent result

Exponent rules

How the exponent calculator works

An exponent calculator evaluates expressions like a^n, where the base is multiplied by itself according to the exponent. This power calculator also handles negative exponent, fractional exponent, and nth root inputs so you can move between powers and radicals without rewriting everything by hand.

Positive powers

2^4 means repeated multiplication: 2 × 2 × 2 × 2 = 16.

Negative exponents

2^-3 becomes the reciprocal 1 / 2^3 = 0.125.

Fractional exponents

81^(3/4) means take the fourth root, then raise the result to the third power.

Repeated multiplication diagram

A whole-number exponent counts how many copies of the base are multiplied.

3^4 = 3 × 3 × 3 × 3 3 3 3 3 × × × Result: 81

Negative exponent diagram

A negative exponent moves the power to the denominator.

5^-2 1 5^2 5^-2 = 1 / 25 = 0.04

Fractional exponents and nth roots

A fractional exponent combines a root and a power. The denominator tells you the root index; the numerator tells you the power. That is why a^(1/2) is a square root and a^(1/3) is a cube root.

The calculator checks the real-number domain before returning an answer. For example, the cube root of -8 is real, but the square root of -8 is not real.

81^(3/4) = (fourth root of 81)^3 Start 81 Fourth root 3 Cube 27 Denominator 4 gives the root. Numerator 3 gives the power.

FAQ

What does a negative exponent mean?

A negative exponent means reciprocal. For example, a^-3 equals 1 / a^3 when a is not zero.

What does a fractional exponent mean?

A fractional exponent a^(p/q) means the qth root of a raised to the p power.

Can this exponent calculator handle negative bases?

Yes, when the real-number result exists. Integer exponents and fractions with odd denominators can work; even roots of negative numbers are not real.