Exponent Calculator
Calculate b^n for any base and exponent, including negative and fractional exponents, with step-by-step working.
About Exponents
An exponent (or power) indicates how many times a base number is multiplied by itself. For example, 2³ = 2 × 2 × 2 = 8. Exponentiation is one of the five fundamental arithmetic operations and appears throughout mathematics, science, finance (compound interest), and computing (binary notation, algorithmic complexity).
Negative exponents represent reciprocals: b^(−n) = 1/b^n. So 2^(−3) = 1/8 = 0.125. Fractional exponents represent roots: b^(1/n) = the n-th root of b. For example, 8^(1/3) = ∛8 = 2. In general, b^(p/q) = (the q-th root of b) raised to the power p. Any non-zero number raised to the power 0 equals 1, by definition.
Very large or very small results are displayed in scientific notation (e.g. 1.024 × 10^30). This compact notation is standard in science and engineering. Laws of exponents let you simplify expressions: b^m × b^n = b^(m+n), (b^m)^n = b^(mn), and (ab)^n = a^n × b^n.
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For a related calculation, use Root Calculator to calculate the nth root of any number, including square roots, cube roots, and arbitrary roots with full working. Alternatively, use Quadratic Formula Calculator to solve ax²+bx+c=0 with the quadratic formula. Find real and complex roots, discriminant, vertex, and factored form.
For the underlying method, read Matrix Operations Explained Simply: Addition, Multiplication, and the Determinant.