How it works
An exponent tells you how many times to multiply the base by itself. Whole exponents are repeated multiplication; negative exponents flip to a fraction; fractional exponents are roots.
result = baseexponent
base−n = 1 ÷ basen
base1/n = the nth root of base
Worked example
2 raised to the 10th power.
- Multiply 2 by itself 10 times: 2×2×2×2×2×2×2×2×2×2.
210 = 1,024.
Common questions
What does a negative exponent mean?
It flips the result to a fraction — base−n equals 1 divided by basen. So 2−3 is 1 ÷ 2³ = 1 ÷ 8 = 0.125.
What does a fractional exponent mean?
It's a root — base1/2 is the square root, base1/3 is the cube root, and so on. base2/3 means "cube root, then square" (or equivalently, square then cube root).
Why does a negative base with a fractional exponent show as undefined?
Some cases do have a real answer (e.g. (−8)1/3 = −2, since −2 cubed is −8), but whether one exists depends on the exact fraction in lowest terms — something a decimal exponent field can't reliably detect. This calculator flags every negative-base, non-whole-exponent case as undefined rather than risk a wrong answer; work those specific cases by hand.