Exponent Calculator
Calculate powers, roots, and exponential expressions.
Calculation Type
The base number
The power to raise the base to
Quick Examples
2^3
Result
Scientific Notation
Standard form
Precision
High precision
Step-by-Step Solution
Mathematical Properties
How it works
An exponent is repeated multiplication: the base multiplied by itself as many times as the exponent says. Negative exponents mean reciprocals, and a zero exponent is always 1.
Exponentiation
bⁿ = b · b · … (n times) b⁻ⁿ = 1 ÷ bⁿ b⁰ = 1
- b
- the base
- n
- the exponent (power)
Worked example
- Compute 2⁵
- 2 × 2 × 2 × 2 × 2
2⁵ = 32.
Good to know
- Multiplying same-base powers adds exponents (2³ × 2² = 2⁵); dividing subtracts them.
- A fractional exponent is a root: b^(1/2) = √b.
- Anything to the power 0 is 1, including very large bases — a handy identity.
Related Calculators
Frequently Asked Questions
What does a negative exponent mean?
A negative exponent means the reciprocal of the positive power: x⁻ⁿ = 1 ÷ xⁿ. For example, 2⁻³ = 1/2³ = 1/8 = 0.125. The base isn't negative — the operation just flips to division.
What is any number raised to the power of zero?
Any nonzero number raised to the power of 0 equals 1. This follows from the quotient rule: xⁿ ÷ xⁿ = xⁿ⁻ⁿ = x⁰, and any number divided by itself is 1. The expression 0⁰ is left undefined in most contexts.
How do fractional exponents work?
A fractional exponent is a root: x^(1/n) is the nth root of x, and x^(m/n) is the nth root of x raised to the mth power. For example, 8^(2/3) = (³√8)² = 2² = 4.
What are the basic exponent rules?
Multiply same bases by adding exponents (xᵃ·xᵇ = xᵃ⁺ᵇ), divide by subtracting them, and raise a power to a power by multiplying exponents ((xᵃ)ᵇ = xᵃᵇ). These rules only apply when the bases match.
Where are exponents used in real life?
Compound interest, population growth, and radioactive decay all follow exponential formulas, and scientific notation uses powers of 10 to express very large or small numbers. Computer storage also scales in powers of 2 (1 KB = 2¹⁰ bytes in binary convention).