Exponent Calculator
Compute bⁿ for any base and exponent. Integer exponents use exact BigInt arithmetic (up to 1000 digits), fractional exponents use floating point. Expanded multiplication, negative exponents and 0⁰ conventions included.
Try an example
Enter a base and an exponent to compute bⁿ.
How to use
- 1
Enter base and exponent
Type the base b and exponent n. Integers and decimals are both supported.
- 2
Read the result
bⁿ is computed — exact BigInt for integer exponents, with expanded multiplication.
- 3
Check the laws
The working panel shows the computation steps, ready to copy and use.
Features
- Integer exponents use exact BigInt arithmetic (up to 1000 digits)
- Expanded multiplication shown (2³ = 2 × 2 × 2) as substituted working
- Negative and fractional exponents supported, 0⁰ = 1 convention included
- Negative base with fractional exponent reported as an error; inputs are never transmitted
Use cases
Check exponent laws
Verify exponent rule calculations (bᵐ × bⁿ = bᵐ⁺ⁿ, etc.) against exact values.
Estimate magnitudes
Quickly compute 10ⁿ and 2ⁿ to gauge digit counts and prevent overflow.
Verify program output
Compare Math.pow or ** operator results against exact big-integer values.
Details
The power bⁿ multiplies the base b by itself n times. Integer exponents are computed exactly with BigInt (arbitrary-precision integers), producing up to 1000 digits without rounding error. For a negative base, the sign depends on the parity of the exponent: even exponents yield a positive result, odd exponents a negative one.
A negative exponent b⁻ⁿ computes 1 ÷ bⁿ (shown as a decimal). A negative base with a fractional exponent yields a complex number and is reported as an error. An exponent of 0 follows the convention 0⁰ = 1 (empty product). Fractional exponents are computed with floating point and shown rounded to six decimal places.
Power computation is the inverse of logarithms (see the log calculator), useful for digit estimation (10ⁿ has n + 1 digits) and for verifying exponent laws (bᵐ × bⁿ = bᵐ⁺ⁿ). Exponents with absolute value above 10000 are rejected. Inputs are never transmitted; all computation happens locally in your browser.
FAQ
What is 0⁰?
By convention, 0⁰ = 1 (the empty product convention). This is consistent with polynomial coefficient calculations and combinatorics, and most textbooks and calculators adopt it. This tool also returns 1.
What happens with a negative base and a fractional exponent?
The result is a complex number, which the tool reports as an error. For example, (-2)^0.5 involves the imaginary unit i.
How large can the numbers get?
Integer bases and exponents use BigInt (arbitrary-precision integers), producing up to 1000 digits without rounding error. The exponent’s absolute value is limited to 10000.
What does a negative exponent mean?
b⁻ⁿ is shorthand for 1 ÷ bⁿ. For example, 2⁻³ = 1 ÷ 2³ = 0.125. Flipping the sign of the exponent gives the reciprocal of the result.
Related Tools
Logarithm Calculator
Compute logarithms in any base, like log₂(8). One-tap bases for 2, 10 and e, with the change-of-base working (ln x ÷ ln b) and a check that bʸ returns x. Common and natural logarithm notes included.
Significant Figures Calculator
Count significant figures, round to a chosen precision, and apply the multiplication/division or addition/subtraction rules. Switch between half-up and JIS Z 8401 half-even rounding; scientific notation is shown alongside.
Prime Factorization
Factor any positive integer into primes. See the product form, exponent form (e.g. 2³×3²) and the number of divisors at once.
Quadratic Equation
Solve ax² + bx + c = 0 with real or complex roots, the discriminant and substitution into the quadratic formula.
All processing happens in your browser. Your files are never uploaded.
Verified: Known values (2^10=1024, (-2)^5=-32, 10^-3=0.001, 2^0.5≈1.414214, 0^0=1), negative base × fractional exponent error and the English page are covered by browser tests
Did you know?
2¹⁰ ≈ 1000, so each power of 2 adds about three decimal digits — a mental shortcut that quickly sizes up integer overflow risks and data volumes in programming.