Raising a number to a power
An exponent tells you how many times to multiply a base by itself. This calculator evaluates base to the power of exponent for any values — whole, negative, or fractional — and shows the result in plain and scientific notation, plus the reciprocal and root forms when they apply.
How exponents work
A positive whole exponent is repeated multiplication: 2 to the 10th is 2 multiplied by itself ten times, which is 1024. A negative exponent is the reciprocal: base to the minus n equals 1 over base to the n. A fractional exponent is a root: base to the one-half is the square root of the base.
Special values
Any nonzero base to the power zero is 1. Zero to a positive power is 0, and zero to a negative power is undefined. A negative base with a non-integer exponent has no real value, since it would require an even root of a negative number.
Related math tools
To go the other way and find the exponent itself, use the logarithm calculator. For equations with a squared term, the quadratic formula calculator.
Worked example
2 to the 10th power multiplies 2 by itself ten times to give 1024, written 1.024 times 10 cubed in scientific notation.
FAQ
What does a fractional exponent mean?
The denominator is a root and the numerator is a power: base to the m over n is the n-th root of base to the m. So 8 to the two-thirds is the cube root of 8 squared, which is 4.
Why is 0 to the 0 ambiguous?
Different limits give different answers, so it is left undefined in general; many contexts adopt 1 by convention.