Square Root & Exponent Calculator

How it works

Powers and roots are fundamental algebraic operations. A power b^n means multiplying b by itself n times (when n is a positive integer); the inverse is the nth root, written ⁿ√x, which finds the number that produces x when raised to the nth power. This calculator handles both, including non-integer exponents, negative bases, and roots of any order.

Negative bases interact tricky with non-integer exponents. (−8)^(1/3) is mathematically −2 (since (−2)³ = −8) but most calculators return NaN because the underlying exponent operation goes through the complex plane. We special-case odd integer roots to return the real value when possible. Even roots of negative numbers are not real; we return NaN there.

Important laws to remember. (a^m)(a^n) = a^(m+n) — multiplying same-base powers adds the exponents. (a^m)^n = a^(mn) — exponentiating an exponent multiplies. a^0 = 1 for any nonzero a. a^(−n) = 1/a^n. a^(1/n) = ⁿ√a. These let you simplify expressions before computing.

Roots and powers convert between each other: ⁿ√(a^m) = a^(m/n). So the cube root of x squared is x^(2/3). For decimal answers, we evaluate using the natural-log identity: a^x = e^(x·ln a). Numerical precision is double-float (~15 significant digits), which is plenty for almost all real-world problems.

For very large powers (like 2^1024) you'll exceed JavaScript's safe-number range and get Infinity. For arbitrary-precision arithmetic use a CAS like Wolfram Alpha. For everyday use, this calculator is fine.