Exponent Calculator
Calculate any base raised to any power, including negative and fractional exponents
Exponent Calculator
Calculate powers and exponents
Compute base raised to any exponent
result = base ^ exponentWhat Is an Exponent?
An exponent (or power) tells you how many times to multiply a base number by itself. Written as bⁿ — "b raised to the power n" — exponents are a compact way to express repeated multiplication. They appear everywhere: compound interest uses A = P(1+r)ⁿ to project growth, areas use side² for squares, volumes use side³ for cubes, and scientific notation uses powers of 10 to express very large or very small numbers without writing out all the zeros.
This calculator handles any combination of base and exponent — positive, negative, or fractional. Negative exponents give you reciprocals: b⁻ⁿ = 1/bⁿ, so 2⁻³ = 1/8. Fractional exponents represent roots: b^(1/2) = √b (square root), b^(1/3) = ∛b (cube root). Any decimal exponent like 0.5 or 0.333 works the same way, letting you compute roots without a separate root calculator.
How to Use the Exponent Calculator
- Enter the base number — this is the number being multiplied (can be positive, negative, or a decimal).
- Enter the exponent — can be any number: positive, negative, a fraction like 1/2, or a decimal like 0.5.
- Click Calculate to compute the result.
- Read the result in both standard notation and scientific notation where applicable.
Exponent Formulas & Rules
bⁿ = b × b × b × ... (n times)
Negative exponent: b⁻ⁿ = 1 / bⁿ
Zero exponent: b⁰ = 1 (for any b ≠ 0)
Fractional exponent: b^(1/n) = ⁿ√b
Exponent rules:
bᵐ × bⁿ = b^(m+n) (product rule)
bᵐ / bⁿ = b^(m−n) (quotient rule)
(bᵐ)ⁿ = b^(m×n) (power rule)
(ab)ⁿ = aⁿ × bⁿ (distributive)Any nonzero number raised to the power of 0 equals 1. The expression 0⁰ is considered indeterminate in mathematics — different fields handle it differently, but in most practical contexts it is treated as 1.
Worked Examples
2¹⁰ = 1,024
Powers of 2 are fundamental in computing. 2¹⁰ = 1,024 is the basis of the binary prefix "kilo" — 1 kilobyte (KB) = 2¹⁰ bytes = 1,024 bytes. Similarly, 2²⁰ = 1,048,576 (1 MB) and 2³⁰ ≈ 1.07 billion (1 GB).
4^0.5 = 2
A fractional exponent of 0.5 is the same as a square root. So 4^0.5 = √4 = 2. This works for any base: 9^0.5 = 3, 25^0.5 = 5, 100^0.5 = 10. Use exponent 0.333 (or 1/3) to compute cube roots.
3⁻² = 1/9 ≈ 0.1111
A negative exponent flips the result into a fraction. 3⁻² = 1/3² = 1/9 ≈ 0.1111. Negative exponents are common in physics and chemistry — for example, acceleration is measured in m·s⁻² (meters per second squared) and concentration in mol·L⁻¹.