Exponent & Root Calculator
Calculate a number raised to a power, or find the nth root of a number.
Power
nth root
How exponents and roots work
Raising a number to a power means multiplying it by itself that many times: base^exponent. This also works for fractional and negative exponents — a negative exponent gives the reciprocal (x^-n = 1/x^n), and a fractional exponent is equivalent to a root.
The nth root of a number x is the value that, raised to the power n, gives back x. It's calculated as x^(1/n). For even-degree roots (square root, 4th root, etc.), negative numbers have no real result, since no real number squared (or raised to any even power) gives a negative value.
Frequently asked questions
What does a negative exponent mean?
A negative exponent means take the reciprocal of the positive power: x^-n = 1 / x^n. For example, 2^-3 = 1/8.
What is a fractional exponent?
A fractional exponent represents a root: x^(1/n) is the nth root of x. For example, 8^(1/3) is the cube root of 8, which is 2.
Why can't I take the square root of a negative number here?
No real number multiplied by itself produces a negative result, so even-degree roots of negative numbers require complex numbers, which this calculator doesn't compute.