Exponent Calculator

A whole positive exponent is repeated multiplication: 2^10 is ten twos multiplied together. A negative exponent is the reciprocal: 2^-3 = 1 / 2^3 = 0.125. A fractional exponent is a root: x^(1/2) is the square root, x^(1/3) the cube root. Anything to the power of 0 is 1, and anything to the power of 1 is itself.

Why is anything to the power of zero equal to 1?

Because dividing a power by itself gives 1, and dividing powers subtracts the exponents. 2^3 / 2^3 is both 1 and 2^0, so 2^0 has to be 1. The one exception is 0^0, which is left undefined.

What does a negative exponent mean?

Take the reciprocal. 10^-2 is 1 / 10^2, which is 0.01. It never makes the answer negative - only smaller.

How do I do a cube root with this?

Enter the number as the base and 0.3333333333 as the exponent, or use the square root calculator for roots you want to be exact. Note that a negative base with a fractional exponent has no real answer here.

What is 2 to the power of 10?

1,024. It comes up constantly in computing, because a kilobyte was originally 1,024 bytes rather than 1,000.