Exponent Calculator

Raise a number to a power, plus squares, cubes and roots.

a raised to b

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a squared (a²)

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a cubed (a³)

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Square root (√a)

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b-th root of a

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Negative powers give reciprocals; fractional powers give roots. Even roots of negatives are undefined in real numbers.

Powers, big and small

An exponent tells you how many times to multiply a base by itself. Whole powers grow fast, negative powers shrink toward zero, and fractional powers reach back into roots.

aᵇ　·　a⁻ⁿ = 1 ÷ aⁿ　·　a^(1/n) = ⁿ√a

The calculator gives the main power plus a few familiar relatives — the square, the cube, the square root and the root matching your exponent — so the connections between powers and roots are clear at a glance.

Worked example

2 raised to the power 10 is 1,024. The same base gives 2² = 4, 2³ = 8, a square root of about 1.414 and a 10th root of about 1.072.

Growth that compounds

Exponents describe anything that multiplies rather than adds: compound interest, population growth, doubling times and the binary scaling of computer memory. Their mirror image, the root, undoes them — which is why roots and fractional powers are the same thing.

Worth remembering

Anything⁰ = 1. For any non-zero base.
Negative flips it. A negative exponent is a reciprocal.
Fractions are roots. a^(1/2) is the square root of a.

Frequently asked questions

What does an exponent mean?

It is repeated multiplication: aᵇ means a multiplied by itself b times. So 2⁴ = 2 × 2 × 2 × 2 = 16.

What about a power of zero or a negative power?

Any non-zero number to the power 0 is 1. A negative power means a reciprocal: a⁻ⁿ = 1 ÷ aⁿ, so 2⁻³ = 1/8.

What is a fractional exponent?

A root. a^(1/n) is the nth root of a, and a^(m/n) is the nth root of a raised to the m. So 8^(1/3) = 2, the cube root of 8.

Why do some roots show as undefined?

Even roots of negative numbers — like the square root of −4 — have no real value. The calculator marks those rather than returning a complex result.