Exponent / Power Calculator
Calculate the result of raising any base number to any exponent with this free online tool. It handles positive, negative, and fractional exponents, and displays the reciprocal of the result for quick reference.
Exponentiation is one of the fundamental operations in mathematics. When you raise a base number b to a power n, written as b^n, you multiply b by itself n times.
Key Rules of Exponents:
- Positive exponent: b^n = b x b x b x ... (n times). For example, 2^5 = 2 x 2 x 2 x 2 x 2 = 32.
- Zero exponent: Any non-zero number raised to the power of 0 equals 1. For example, 7^0 = 1.
- Negative exponent: b^(-n) = 1/(b^n). For example, 2^(-3) = 1/8 = 0.125.
- Fractional exponent: b^(1/n) = the nth root of b. For example, 8^(1/3) = cube root of 8 = 2. More generally, b^(m/n) = (nth root of b)^m.
- Product rule: b^m x b^n = b^(m+n).
- Power rule: (b^m)^n = b^(m x n).
Exponents are used extensively in science (scientific notation), finance (compound interest), computer science (binary systems), and physics (exponential growth and decay).