Exponent Calculator
Calculate base^exponent for any real base and exponent, including negative and fractional powers.
Each step multiplies by 2 again — watch how fast 2^10 builds up to 1,024 from 2^1.
ƒShow your work
- 12^10 = 1,024
- 22 multiplied by itself 10 times: 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1,024
About the Exponent Calculator
Exponents describe repeated multiplication, and once you move past whole-number powers like 2³, the rules get genuinely easy to second-guess — what does a negative exponent do, what does raising something to the power of 0 give you, and what on earth does a fractional exponent even mean. This calculator handles all of it: positive, negative, zero, and fractional exponents, on any base.
It gets used for the straightforward case — checking 2^10 while working through a computer science problem, or verifying compound growth math — as much as for the confusing edge cases, where seeing the actual number the rule produces is often what makes the rule finally click.
How it’s calculated
A positive integer exponent means repeated multiplication: 2^4 = 2 × 2 × 2 × 2 = 16. Any nonzero number raised to the power of 0 equals exactly 1 — this isn't an arbitrary convention, it falls directly out of the pattern of dividing consecutive powers (2³/2³ = 2^0 = 1).
A negative exponent means 'take the reciprocal': base^(−n) = 1 / base^n. So 2^(−3) = 1/2³ = 1/8. It's the natural extension of the pattern where each step down in the exponent divides by the base again — 2², 2¹, 2⁰, 2^(−1) is 4, 2, 1, 0.5, each half the last.
A fractional exponent combines a power and a root: base^(a/b) means take the b-th root of base, then raise it to the a-th power (the order doesn't matter, both give the same result). So base^(1/2) is the square root, base^(1/3) is the cube root, and base^(3/2) is the square root of base, cubed.
Frequently asked questions
What does a negative exponent mean?
It means take the reciprocal of the positive-exponent version: base^(−n) = 1/base^n. For example, 5^(−2) = 1/5² = 1/25 = 0.04. The negative sign flips it to a fraction, it doesn't make the result negative.
What is any number raised to the power of 0?
It's always 1, as long as the base isn't 0 itself (0^0 is a special case that's mathematically undefined/context-dependent). This falls out of the pattern of dividing consecutive powers of the same base.
What does a fractional exponent mean?
It represents a root. base^(1/n) is the nth root of base, so base^(1/2) is a square root and base^(1/3) is a cube root. A fraction like 3/2 in the exponent combines both: take a root, then raise to a power (or the other way around — the result is the same).
Why is 0 raised to a negative exponent undefined?
Because a negative exponent means taking the reciprocal, and the reciprocal of 0 (1/0) is undefined — division by zero isn't a valid operation, so the expression has no defined value.
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