Exponent Calculator

Exponentiation is a mathematical operation, written as a^n, involving the base a and an exponent n. In the case where n is a positive integer, exponentiation corresponds to repeated multiplication of the base, n times.

Basic exponent laws: When exponents that share the same base are multiplied, the exponents are added (a^n × a^m = a^(n+m)). When an exponent is negative, the negative sign is removed by reciprocating the base (a^(−n) = 1/a^n). When exponents are divided, the exponents are subtracted (a^m / a^n = a^(m−n)). When exponents are raised to another exponent, the exponents are multiplied ((a^m)^n = a^(m×n)). When multiplied bases are raised to an exponent, the exponent is distributed to both bases ((a × b)^n = a^n × b^n).

When an exponent is 1, the base remains the same (a^1 = a). When an exponent is 0, the result of the exponentiation of any base will always be 1, although some debate surrounds 0^0 being 1 or undefined. When an exponent is a fraction where the numerator is 1, the nth root of the base is taken.