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Power and Root Calculator

Calculate powers, square roots, cube roots, and nth roots easily.

Powers and Roots Explained

Exponents, square roots, and nth roots

A power (exponent) means multiplying a number by itself a set number of times. 2³ = 2 × 2 × 2 = 8. The base is 2, the exponent is 3, and 8 is the result. Square root (√): The inverse of squaring. √25 = 5 because 5² = 25. Every positive number has two square roots: +5 and -5, though conventionally we use the positive one. Cube root (∛): The inverse of cubing. ∛27 = 3 because 3³ = 27. Unlike square roots, cube roots of negative numbers are real: ∛-8 = -2. Fractional exponents: x^(1/n) = nth root of x. So 8^(1/3) = ∛8 = 2. And x^(m/n) = (nth root of x)^m. So 8^(2/3) = (∛8)² = 4. Negative exponents: x^(-n) = 1/xⁿ. So 2^(-3) = 1/8 = 0.125. Any number to the power of 0 equals 1: x⁰ = 1.

Frequently Asked Questions

Common questions about powers and roots

An exponent indicates how many times a number (base) is multiplied by itself. For example, 2³ = 2 × 2 × 2 = 8. Here 2 is the base and 3 is the exponent.

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