Exponent / Power Calculator

A negative exponent means the reciprocal of the positive power: b⁻ⁿ = 1/bⁿ. For example, 2⁻³ = 1/2³ = 1/8 = 0.125. Negative exponents appear frequently in scientific notation for very small numbers, such as 10⁻⁹ = 0.000000001 (one nanometre).

A fractional exponent represents a root: b^(1/n) = ⁿ√b. For example, 8^(1/3) = ∛8 = 2. Combined: b^(m/n) = (ⁿ√b)^m. So 8^(2/3) = (∛8)² = 2² = 4. Fractional exponents unify the concepts of powers and roots into a single notation.

By the pattern of dividing by the base: 2³=8, 2²=4, 2¹=2, 2⁰=1 (dividing 2 by 2). Also consistent with the exponent rule b^m ÷ b^m = b^(m-m) = b⁰, which must equal 1 because any number divided by itself is 1.