Exponent Calculator
Enter a base and an exponent below to instantly calculate the result, including negative and fractional exponents.
How Exponents Work
b^n means multiply b by itself n times. The rules extend naturally to zero, negative, and fractional exponents rather than needing separate definitions for each case.
Worked example
Calculate 3^4.
3 × 3 × 3 × 3 = 81
3^4 = 81
Frequently Asked Questions
What does an exponent mean?
An exponent tells you how many times to multiply the base by itself. 2^4 means 2 × 2 × 2 × 2 = 16.
What does a negative exponent mean?
A negative exponent means take the reciprocal: b^(-n) = 1 / b^n. For example, 2^(-3) = 1/8.
What does an exponent of 0 give you?
Any nonzero number raised to the power of 0 equals 1. This isn't arbitrary — it falls directly out of the pattern of dividing successive powers by the base (2³=8, 2²=4, 2¹=2, 2⁰=1).
What does a fractional exponent mean?
A fractional exponent represents a root. b^(1/2) is the square root of b, and b^(1/3) is the cube root. b^(m/n) means take the nth root of b, then raise it to the mth power.
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