Exponent Calculator
Raise any number to any power – positive, negative or fractional exponents. Whole-number powers are exact, even when the result has thousands of digits.
What an exponent means
The exponent says how many times the base is multiplied by itself: 2¹⁰ = 2 × 2 × … × 2 = 1,024. Any number to the power 1 is itself, and any non-zero number to the power 0 is 1.
Negative and fractional exponents
- A negative exponent means one over the power: 2⁻³ = 1 / 2³ = 0.125.
- A fraction means a root: 9^(1/2) = √9 = 3 and 8^(1/3) = ∛8 = 2.
- 8^(2/3) is the cube root of 8², which is 4.
Rules for exponents
| Rule | Example |
|---|---|
| aᵐ · aⁿ = aᵐ⁺ⁿ | 2³ · 2⁴ = 2⁷ = 128 |
| aᵐ / aⁿ = aᵐ⁻ⁿ | 5⁶ / 5⁴ = 5² = 25 |
| (aᵐ)ⁿ = aᵐⁿ | (3²)³ = 3⁶ = 729 |
| (a · b)ⁿ = aⁿ · bⁿ | (2 · 5)³ = 1,000 |
Very large powers
Most calculators switch to rounded scientific notation after about 15 digits. Here, whole-number bases with whole-number exponents up to 20,000 are calculated exactly: 2¹⁰⁰ = 1,267,650,600,228,229,401,496,703,205,376 – 31 digits. Results with more than 40 digits are shown in scientific notation, and all digits are listed below them.
Frequently asked questions
What is 2 to the power of 10?
1,024.
What does a negative exponent mean?
One divided by the positive power. 10⁻² = 1 / 10² = 0.01.
What is 0 to the power of 0?
By convention it is taken as 1 in algebra and combinatorics, and the calculator follows that. In calculus it is treated as undefined.