Raise any number to any power, including negative and fractional exponents.
An exponent calculator works out powers like 2¹⁰, 5⁻² and 27^(2/3) in one step. Enter the base and the exponent, and you get the answer, the same value in scientific notation, and a short explanation of the rule behind it, from repeated multiplication to roots.
Quick answer: an exponent tells you how many times to multiply a number by itself. 2⁵ = 2 × 2 × 2 × 2 × 2 = 32. A negative exponent means 1 divided by the power, so 5⁻² = 1/25 = 0.04. A fractional exponent means a root, so 16^(1/2) = √16 = 4.
How to Use the Exponent Calculator
- Enter the base (x), the number being multiplied.
- Enter the exponent (n), the power. Negative and decimal exponents are allowed, such as −2 or 0.5.
- Read the result, the scientific notation, and the step that explains it.
For very large or very small results, the scientific notation is easier to read. The scientific notation calculator converts between the two forms.
Exponent Rules
| Rule | Formula | Example |
|---|---|---|
| Product rule | xᵃ × xᵇ = xᵃ⁺ᵇ | 2³ × 2⁴ = 2⁷ = 128 |
| Quotient rule | xᵃ ÷ xᵇ = xᵃ⁻ᵇ | 5⁶ ÷ 5⁴ = 5² = 25 |
| Power of a power | (xᵃ)ᵇ = xᵃᵇ | (3²)³ = 3⁶ = 729 |
| Zero exponent | x⁰ = 1 | 7⁰ = 1 |
| Negative exponent | x⁻ⁿ = 1 ÷ xⁿ | 5⁻² = 1/25 = 0.04 |
| Fractional exponent | x^(1/n) = ⁿ√x | 8^(1/3) = ∛8 = 2 |
| Power of a product | (xy)ⁿ = xⁿyⁿ | (2 × 3)² = 4 × 9 = 36 |
Exponent Examples
2¹⁰ = 2 multiplied by itself 10 times = 1,024. This is why a kilobyte is sometimes counted as 1,024 bytes.
5⁻² = 1 ÷ 5² = 1 ÷ 25 = 0.04.
27^(2/3): the 3 in the denominator means a cube root, and the 2 means square it. ∛27 = 3, and 3² = 9.
(−2)³ = −2 × −2 × −2 = −8. An odd power of a negative number is negative. An even power is positive.
0.5³ = 0.125. Raising a number between 0 and 1 to a power makes it smaller.
Exponents in Real Life
- Compound growth: $1,000 growing at 5% a year for 10 years is 1,000 × 1.05¹⁰ ≈ $1,628.89.
- Computer storage: each extra bit doubles the number of values, so 8 bits give 2⁸ = 256 values.
- Area and volume: a square’s area is side², and a cube’s volume is side³.
- Population and bacteria growth, which double at regular intervals.
Mistakes to Avoid
- Multiplying the base by the exponent. 3⁴ is 81, not 12.
- Forgetting brackets with negatives. −3² = −9, but (−3)² = 9. The exponent only applies to what it touches.
- Adding exponents when the bases differ. 2³ × 3² cannot be combined into one power.
- Treating a negative exponent as a negative answer. 2⁻³ = 1/8, which is positive.
Related Math Tools
- For square roots, cube roots and simplified radicals, use the square root calculator.
- For longer expressions with powers, trig and logs, use the scientific calculator.
Exponent Calculator FAQs
What is anything to the power of 0?
Any non-zero number to the power 0 is 1. That follows from the quotient rule: x³ ÷ x³ = x⁰, and anything divided by itself is 1. 0⁰ is a special case that is usually defined as 1 in algebra.
What does a fractional exponent mean?
The bottom of the fraction is the root and the top is the power. x^(3/2) means the square root of x, cubed.
Why does a negative base with a decimal exponent give an error?
Because it has no real answer. (−8)^0.5 would be the square root of −8, which is not a real number. The calculator tells you when this happens.
How do I type an exponent on a keyboard?
Use the caret symbol: 2^10. The scientific calculator accepts this format.
How we checked this page: every example and every row of the rules table was worked by hand and matches the calculator.