numvana

Exponent & Root Calculator

Raise a number to any power and find its corresponding root — x^y and the y-th root of x — from the same two inputs.

x^y
512
y-th root of x
2

How it works

x^y is plain exponentiation: x multiplied by itself y times (or the general power function for non-integer y). The y-th root of x is the inverse operation — the number that, raised to the y-th power, gives back x — which is the same as x^(1/y).

A negative x only has a real y-th root when y is an odd whole number (e.g. the cube root of −27 is −3, since (−3)³ = −27). For a negative x with an even root degree, no real number solves it — √−8 isn't a real number — so this calculator reports that instead of returning a meaningless result.

FAQ

Why does a negative base with an even exponent fail for the root?

Any real number raised to an even power is non-negative, so no real number can have an even-degree root that comes out negative. The power calculation itself still works fine for a negative base (e.g. (−2)² = 4) — it's specifically the root direction that has no real answer in that case.

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