Powers and roots
A power is a number multiplied by itself several times, and a root is the reverse. Also use it to write very large and very small numbers briefly.
The explanation is shown. Quick: one number in, the answer out. Advanced: a table of the neighbouring exponents and the answer in scientific notation.
Your numbers
Answer
2^10
1,024
Square number a²
4
Cube number a³
8
How to work it out
- 12^10 = 1,024
The formula
aⁿ = a · a · … · a
n factors, all of which are a.
a⁰ = 1 · a⁻ⁿ = 1 / aⁿ
aⁿ · aᵐ = aⁿ⁺ᵐ · (aⁿ)ᵐ = aⁿ·ᵐ
The rules of exponents.
ⁿ√a = a^(1/n)
A root is a power with a fraction as the exponent.
In depth: more numbers and “what if”
Powers of 2
| Exponent | Value | Scientific notation |
|---|---|---|
| 2^7 | 128 | 1.28 · 10^2 |
| 2^8 | 256 | 2.56 · 10^2 |
| 2^9 | 512 | 5.12 · 10^2 |
| 2^10 | 1,024 | 1.024 · 10^3 |
| 2^11 | 2,048 | 2.048 · 10^3 |
| 2^12 | 4,096 | 4.096 · 10^3 |
| 2^13 | 8,192 | 8.192 · 10^3 |
More: Numbers and percentages
- PercentPercentage of, how many per cent, percentage change, discount and VAT.
- FractionsAdd, subtract, multiply and divide fractions — and simplify the answer.
- Primes and divisorsIs it a prime? Prime factors, divisors, GCD and LCM.
- Rounding and estimatingRound to decimals, tens or significant figures — and make an estimate.
- Order of operationsEnter a calculation and see it worked out step by step in the right order.
- Number systems and Roman numeralsBinary, hexadecimal and Roman numerals — converted both ways with working.