What is an exponent?
An exponent tells you how many times to multiply a number (the base) by itself. In 2^10 the base is 2 and the exponent is 10, so the answer is 2 multiplied by itself ten times, which is 1,024.
Exponents can also be zero, negative or fractional. This calculator handles all of these and shows the result in ordinary and scientific notation, together with the reciprocal, square, cube and square root of the base.
How it is calculated
a^n = a × a × … × a (n times)
a^0 = 1
a^(−n) = 1 ÷ a^n
a^(1/n) = n-th root of a
Worked example
Four cases
- 2^10
- 1024
- 5^−2 (a reciprocal)
- 0.04
- 27^(1/3) (a cube root)
- 3
- 10^6
- 1000000
Laws of exponents
| Rule | Example |
|---|---|
| a^m × a^n = a^(m+n) | 2³ × 2⁴ = 2⁷ = 128 |
| a^m ÷ a^n = a^(m−n) | 5⁶ ÷ 5² = 5⁴ = 625 |
| (a^m)^n = a^(mn) | (3²)³ = 3⁶ = 729 |
| (ab)^n = a^n × b^n | (2×5)² = 4 × 25 = 100 |
A sign mistake worth knowing
−2² and (−2)² are not the same. Without brackets, exponentiation applies to the 2 first, then the minus sign, giving −2² = −4. With brackets around the −2, you square the negative number itself: (−2)² = 4. This calculator's base field is the number being raised, equivalent to always having the brackets.