How are roots of negative numbers handled?

For odd roots (like a cube root), the calculator preserves the sign of a negative input, since a real odd root of a negative number exists (e.g. the cube root of −8 is −2). Even roots of negative numbers are not real, so those aren't returned.

Can the exponent be a fraction or negative number?

Yes. A fractional exponent computes a root (base^(1/2) is the same as a square root), and a negative exponent computes the reciprocal of the positive power (base^−n = 1 ÷ base^n).

Exponent & Root Calculator

Calculate powers (exponents) and nth roots.

How this is calculated

Exponent: base^exponent. Root: value^(1/degree), sign-preserving for odd roots of negative numbers.

Assumptions used in this calculation

Root sign convention: Odd-degree roots of negative numbers return the real negative result; even-degree roots of negative numbers are not computed since they aren't real.

About this calculator

Calculates exponents (base raised to a power) and nth roots, consolidated into one calculator since they're inverse operations of each other.

Worked example

2^10

Result: 1024

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About this calculator

Frequently asked questions

How are roots of negative numbers handled?

Can the exponent be a fraction or negative number?

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