Exponent and Root Calculator (Power, Square Root, Cube Root, n-th Root)

The tool has two parts: powers (xʸ) and roots (ⁿ√a). Powers work with whole, fractional and negative exponents; the root part returns the square root, the cube root and the n-th root you choose for the same number.

Rules and formulas

• xʸ: for a whole y, x multiplied by itself y times; x⁰ = 1, x⁻ʸ = 1 / xʸ
• A fractional exponent is a root: x^(1/n) = ⁿ√x, x^(m/n) = (ⁿ√x)ᵐ
• ⁿ√a = a^(1/n); √a = a^(1/2), ∛a = a^(1/3)
• A negative a has a real root only for an odd whole n: ⁿ√a = −ⁿ√|a| (e.g. the fifth root of −32 is −2)
• A negative base is raised only to whole exponents: (−2)³ = −8, but (−8)^0.5 is not a real number

Example: 2¹⁰ = 1024; the cube root of 27 is 3 and its square root √27 ≈ 5.19615242. 1.5⁻² = 1 / 2.25 ≈ 0.44444444.

Undefined cases (a negative base with a fractional exponent, zero to a negative power, an even root of a negative number) are reported as 0 with the "computed = 0" flag instead of an error. Powers above roughly 10²⁹ are not computed either.

Extra example: 1000^0.4 ≈ 15.84893192. The fifth root of −32 is −2; the cube root of the same number is ≈ −3.17480210, while its square root is not real and shows 0.

How to read the result: check the “Power computed” and “n-th root is real” flags first: 1 means the result is valid, 0 means it is undefined or not a real number and the related value is shown as 0. Results are rounded to 8 decimals; irrational values (such as √27) are approximations. The cube root is always real for negative numbers; the square root and other even roots are computed only for non-negative numbers.