worldofcalcsExponent Calculator
Result
256
2⁸ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256
What is an exponent?
An exponent (or power) says how many times to multiply a number, the base, by itself: 2⁸ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256. A negative exponent means the reciprocal, and a fractional exponent means a root. This calculator gives exact answers for whole-number powers, however many digits they have, and the scientific notation for very large or small results.
Laws of exponents
aᵐ × aⁿ = aᵐ⁺ⁿ · aᵐ ÷ aⁿ = aᵐ⁻ⁿ · (aᵐ)ⁿ = aᵐⁿ · a⁰ = 1 · a⁻ⁿ = 1 ÷ aⁿ · a^(1/n) = ⁿ√a
These laws hold for any non-zero base. They're the basis of the Class 8 'Exponents and Powers' chapter and of scientific notation.
Good to know
- Any non-zero number to the power 0 is 1.
- 2¹⁰ = 1,024 is close to 1,000, which is why a kilobyte is sometimes 1,024 bytes.
- Scientific notation writes numbers as a × 10ⁿ with 1 ≤ a < 10: the speed of light is about 3 × 10⁸ m/s.
- A negative base with a fractional exponent, such as (−8)^0.5, has no real answer; (−8)^(1/3) = −2 is a special case of an odd root.
- Compound interest grows by a power: an amount at 10% a year for 5 years is multiplied by 1.1⁵ ≈ 1.61.
Worked examples
- 2⁸ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256
- 5⁻² = 1 ÷ 5² = 1 ÷ 25 = 0.04
- 27^(1/3) = ∛27 = 3
- 2¹⁰ × 2⁵ = 2¹⁵ = 32,768
- (−3)³ = −27, but (−3)⁴ = 81: an odd power keeps the sign
Powers of 2, 3 and 10
Values worth knowing by heart.
| n | 2ⁿ | 3ⁿ | 10ⁿ |
|---|---|---|---|
| 0 | 1 | 1 | 1 |
| 1 | 2 | 3 | 10 |
| 2 | 4 | 9 | 100 |
| 3 | 8 | 27 | 1,000 |
| 4 | 16 | 81 | 10,000 |
| 5 | 32 | 243 | 1,00,000 |
| 6 | 64 | 729 | 10,00,000 |
| 7 | 128 | 2,187 | 1,00,00,000 |
| 8 | 256 | 6,561 | 10,00,00,000 |
| 9 | 512 | 19,683 | 1,00,00,00,000 |
| 10 | 1,024 | 59,049 | 10,00,00,00,000 |
Each column multiplies by its base going down.