Power and root calculator
A power is repeated multiplication and a root is its inverse: if 2⁵ is 32, then the fifth root of 32 is 2. A fractional exponent is a root — x^(1/2) is exactly the square root of x.
Power
1,024
- Square root of the number
- 1.414214
- Nth root of the number
- 1.071773
Rates and thresholds
- Power
- 2⁵ = 32
- Square root
- √144 = 12
- Fractional exponent
- x^(1/n) = ⁿ√x
- Negative exponent
- x⁻ⁿ = 1 ÷ xⁿ
Why is any number to the power of zero one?
Because dividing powers subtracts exponents: 2⁵ ÷ 2⁵ is 2⁰, and the same operation is a number divided by itself, which is one. The rule keeps exponent arithmetic consistent and holds for every number except zero, where 0⁰ is left undefined.
Can you take the square root of a negative number?
Not within the real numbers: no number multiplied by itself gives a negative result, since minus times minus and plus times plus are both positive. Odd roots are the exception — the cube root of −8 is −2, because −2 × −2 × −2 = −8.
Related calculators
- Percentage calculator
- Percentage change calculator
- Discount calculator
- Average calculator
- Circle calculator
- Triangle calculator