Exponent Calculator

An exponent (power) says how many times to multiply the base by itself. 2^3 = 2 x 2 x 2 = 8. The base is the number being multiplied, the exponent is how many times. Notation: a^n, a^n, or pow(a,n). Special cases: a^0 = 1, a^1 = a, a^-1 = 1/a.

a^(-n) = 1/a^n. Example: 2^(-3) = 1/2^3 = 1/8 = 0.125. Negative exponents represent fractions/reciprocals. 10^(-3) = 0.001 (milli-). In scientific notation: 1.5 x 10^(-6) = 0.0000015 (1.5 microseconds).

a^(1/2) = sqrt(a). a^(1/3) = cube root of a. a^(m/n) = nth root of a^m = (nth root of a)^m. Examples: 9^(1/2) = 3, 8^(1/3) = 2, 16^(3/4) = (16^(1/4))^3 = 2^3 = 8. Fractional exponents connect powers and roots.

Product: a^m x a^n = a^(m+n). Quotient: a^m / a^n = a^(m-n). Power of power: (a^m)^n = a^(mn). Power of product: (ab)^n = a^n x b^n. Zero exponent: a^0 = 1 (for a ≠ 0). Negative: a^(-n) = 1/a^n.

Squaring a number means raising it to the power 2: n^2 = n x n. The result is the area of a square with side n. Cubing means n^3 = n x n x n — the volume of a cube with side n. Perfect squares: 1,4,9,16,25,36... Perfect cubes: 1,8,27,64,125...