Exponent and Root Calculator
Raise a number to any power or take any root, including negative and fractional exponents.
Exponents
An exponent says how many times to multiply a number by itself: 2¹⁰ = 2 × 2 × … × 2 (ten times) = 1,024.
Exponent rules
| Rule | Example |
|---|---|
| xᵃ × xᵇ = xᵃ⁺ᵇ | 2³ × 2⁴ = 2⁷ = 128 |
| xᵃ ÷ xᵇ = xᵃ⁻ᵇ | 5⁶ ÷ 5⁴ = 5² = 25 |
| (xᵃ)ᵇ = xᵃᵇ | (3²)³ = 3⁶ = 729 |
| x⁰ = 1 | 7⁰ = 1 |
| x⁻ⁿ = 1 ÷ xⁿ | 2⁻³ = 1/8 = 0.125 |
| x^(1/n) = ⁿ√x | 27^(1/3) = 3 |
Roots
A root reverses an exponent. The cube root of 27 is 3 because 3³ = 27. Even roots (square root, fourth root) of negative numbers are not real numbers, while odd roots of negative numbers are: the cube root of −8 is −2.
Where exponents appear
- Compound interest: money grows by (1 + r)ⁿ.
- Computing: storage sizes are powers of 2, such as 2¹⁰ = 1,024.
- Science: scientific notation uses powers of 10.
- Area and volume: squaring and cubing lengths.
Frequently asked questions
What is any number to the power of 0?
Any non-zero number raised to the power 0 equals 1. 0⁰ is usually defined as 1 in algebra but is treated as undefined in some contexts.
What does a negative exponent mean?
It means the reciprocal: x⁻ⁿ = 1 ÷ xⁿ. For example, 10⁻² = 0.01.
How do I calculate a fractional exponent?
x^(a/b) is the b-th root of x raised to the power a. For example, 8^(2/3) = (cube root of 8)² = 4.
Last reviewed Oct 20, 2026. Results are estimates; check important decisions with a qualified professional.