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 |