About the Exponent Calculator
What is the Exponent Calculator?
An exponent (or power) tells you how many times to multiply a base by itself: 2¹⁰ = 2 × 2 × … × 2 (ten times) = 1,024. Exponents make very large and very small numbers manageable and describe anything that compounds, such as interest, population or bacterial growth.
The calculator accepts any real base and exponent. Negative exponents give reciprocals (2⁻³ = 1/8), fractional exponents give roots (16^0.5 = 4), and very large or very small results are shown in scientific notation.
How to use the Exponent Calculator
- Base (a) (sample: 2)
- Exponent (n) — can be negative or a decimal (0.5 means square root). (sample: 10)
- Press Calculate Power (results also refresh as you type). The result card shows the Result, along with Scientific notation and Reciprocal a⁻ⁿ.
Formula used
aⁿ = a × a × … × a (n times)
- a = the base
- n = the exponent (power)
a⁻ⁿ = 1 ÷ aⁿ, a^(1/n) = ⁿ√a and a⁰ = 1 for any a ≠ 0. A negative base with a fractional exponent, such as (−8)^0.5, has no real answer.
Worked example
These are the sample values already filled in the calculator above, and the result it returns for them:
| Input | Sample value |
|---|---|
| Base (a) | 2 |
| Exponent (n) | 10 |
| Result | Value |
|---|---|
| aⁿ | 1,024 |
| Scientific notation | 1.024000e+3 |
| Reciprocal a⁻ⁿ | 9.765625e-4 |
Laws of exponents
- aᵐ × aⁿ = aᵐ⁺ⁿ
- aᵐ ÷ aⁿ = aᵐ⁻ⁿ
- (aᵐ)ⁿ = aᵐⁿ
- (a × b)ⁿ = aⁿ × bⁿ
- a⁰ = 1 (a ≠ 0)
Tips for using the Exponent Calculator
- Scientific notation such as 1.024000e+3 means 1.024 × 10³ = 1,024.
- Compound growth is an exponent: 1,00,000 growing at 12% a year for 10 years becomes 1,00,000 × 1.12¹⁰ ≈ 3,10,585.
- (−2)⁴ = 16 but −2⁴ = −16 — brackets decide whether the minus sign belongs to the base.