Exponent calculator
Raising to the power 0.5 is the same as taking a square root, and to 1/3 is a cube root. It follows from the rule that multiplying powers adds the exponents: x^0.5 × x^0.5 = x^1, so x^0.5 must be the thing that gives x when multiplied by itself. Negative exponents follow the same logic in reverse — x^−1 is 1/x, because x^1 × x^−1 = x^0 = 1.
An exponent is repeated multiplication: 2^10 is 1,024. A negative exponent gives the reciprocal, so 2^−1 is 0.5. A fractional exponent is a root, so 9^0.5 is 3.
How to use exponents
Three rules cover almost all exponent arithmetic. Multiplying powers of the same base adds the exponents. Dividing subtracts them. Raising a power to a power multiplies them. Everything else — why anything to the power zero is one, why negative exponents are reciprocals, why fractional exponents are roots — falls out of those three rules being applied consistently rather than being separate facts to memorise.
Questions
1,024 — which is why a kilobyte is 1,024 bytes rather than 1,000.