Exponent Calculator

An exponent tells you how many times to multiply the base by itself. 2^5 = 2 x 2 x 2 x 2 x 2 = 32. The base is 2, the exponent is 5. Any number to the power of 0 is 1 (except 0^0 which is debated). Any number to the power of 1 is itself. The calculator handles all these cases.

A negative exponent means "take the reciprocal." 2^(-3) = 1/(2^3) = 1/8 = 0.125. The negative sign does not make the result negative — it creates a fraction. 5^(-2) = 1/25 = 0.04. This rule works for any base and makes exponent arithmetic consistent across all integer powers.

Yes — fractional exponents represent roots. x^(1/2) = square root of x, x^(1/3) = cube root, x^(2/3) = cube root of x squared. Enter decimal exponents like 0.5 or fractions like 1/3. The calculator handles any real-valued exponent with full decimal precision.

Large results (like 2^100 = 1.267 x 10^30) are displayed in scientific notation because the full number would be impractically long. The calculator shows both scientific notation and the full number when feasible. Very large exponents can exceed JavaScript's number precision — the tool warns when this occurs.

Key exponent rules: x^a * x^b = x^(a+b), x^a / x^b = x^(a-b), (x^a)^b = x^(a*b), (xy)^a = x^a * y^a, x^0 = 1, x^(-a) = 1/x^a. These rules let you simplify complex exponential expressions. The calculator applies these rules when showing step-by-step solutions.