Exponent Calculator
Work out a number raised to a power, like 2¹⁰ or 5⁻². Whole-number powers show every digit, even when the answer is hundreds of digits long.
About this tool
Whole-number bases and exponents are worked out exactly, up to 5,000 digits. Negative and fractional exponents use ordinary decimal arithmetic, accurate to about 15 significant digits.
Raise a number to a power: squares, cubes, powers of 2 and 10, negative powers and fractional powers. When the base and exponent are whole numbers, the calculator works out every digit exactly, so 2⁶⁴ shows all 20 digits instead of a rounded value.
How to use the Exponent Calculator
- Type the base, the number being multiplied.
- Type the exponent, the number of times to multiply it. Negative and decimal exponents work.
- Read the result, how many digits it has, its scientific notation and its reciprocal.
2¹⁰, 2⁶⁴ and 5⁻²
2¹⁰ = 2 × 2 × … × 2 (ten times) = 1,024. 2⁶⁴ = 18,446,744,073,709,551,616, a 20-digit number. A negative exponent means one over the power: 5⁻² = 1 ÷ 5² = 1 ÷ 25 = 0.04. A fractional exponent is a root: 9^0.5 = √9 = 3.
Powers of 2
Exact values from this calculator.
| Power | Value | Digits |
|---|---|---|
| 2¹⁰ | 1,024 | 4 |
| 2²⁰ | 1,048,576 | 7 |
| 2³² | 4,294,967,296 | 10 |
| 2⁶⁴ | 18,446,744,073,709,551,616 | 20 |
| 2¹⁰⁰ | 1,267,650,600,228,229,401,496,703,205,376 | 31 |
The rules of exponents
aⁿ means a multiplied by itself n times. Anything to the power 0 is 1, so 7⁰ = 1. A negative exponent turns the answer into a fraction: a⁻ⁿ = 1 ÷ aⁿ. A fractional exponent is a root: a^(1/2) is the square root and a^(1/3) is the cube root. When you multiply powers of the same base you add the exponents (2³ × 2⁴ = 2⁷), and when you raise a power to a power you multiply them ((2³)² = 2⁶).
Common mistakes
- Treating −3² as (−3)². Strictly, −3² = −9 because the power applies before the minus sign; (−3)² = 9. Type the base as −3 here to get 9.
- Thinking a negative exponent makes the answer negative. 5⁻² is 0.04, a small positive number.
- Expecting a real answer for a negative base with a fractional exponent, such as (−8)^0.5. There isn’t one.
Frequently asked questions
What is 2 to the power of 10?
1,024.
What is any number to the power of 0?
1, for any base except 0, where 0⁰ is usually taken as 1 in algebra but left undefined in some contexts.
How big can the numbers get?
Whole-number powers are shown exactly up to 5,000 digits. Other results use ordinary decimal arithmetic, accurate to about 15 significant digits.
How do I type a fractional exponent?
As a decimal, for example 0.5 for a square root or 0.25 for a fourth root.