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Math Power Calculator — Exponentiation (b^n)

Compute any base raised to any power — integer, decimal, negative or zero — and see the step-by-step working plus a curve of the power function.
The number to raise to a power (can be negative or decimal)
The power to raise the base to (integer, decimal or negative)
Result (b^n)
1,024

The base raised to the given exponent

Reciprocal (b^−n)
0.00097656
Square root of base (b^½)
1.414214
Cube root of base (b^⅓)
1.259921
Step-by-step
1

Identify base and exponent

b = 2, n = 10
2

Apply exponentiation

b^n = 2 ^ 10
=

Result

= 1,024
b^10
Step by step
  1. 1

    Base

    b = 2 = 2
  2. 2

    Exponent

    n = 10 = 10
  3. 3

    b raised to the power n

    2 ^ 10 = 1,024
Results are estimates for general information only and are not professional advice — always verify important results independently before relying on them. Read the full disclaimer.
Quick answer

How does this calculator work?

b^n raises any base to any exponent. Special cases: b^0 = 1, b^(−n) = 1/b^n, b^(½) = √b. The calculator handles integers, decimals and negative exponents, shows step-by-step working, and plots the power function b^x to illustrate exponential growth or decay.

Formula
b^n • b^(−n) = 1 / b^n • b^(½) = √b • b^0 = 1 (for b ≠ 0)
How this is calculated

Exponentiation (written b^n or bⁿ) is repeated multiplication for positive integers: 2^4 = 2 × 2 × 2 × 2 = 16. The rule extends naturally to other cases: b^0 = 1 for any non-zero base; b^(−n) = 1 / b^n (reciprocal); b^(1/n) = the n-th root of b; and b^(p/q) = the q-th root of b^p.

This calculator uses IEEE-754 double-precision floating-point arithmetic (Math.pow), accurate to about 15–16 significant digits. Very large exponents overflow to ±Infinity; results are left undefined in that case. For negative bases with non-integer exponents, the result is complex (imaginary) and is not computed here — use a complex-number calculator for those cases.

The XY curve shows b^x as x sweeps from 0 to n, illustrating exponential growth (b > 1) or exponential decay (0 < b < 1) visually.

Frequently asked questions

b^(−n) = 1 / b^n. For example, 2^(−3) = 1 / 2^3 = 1 / 8 = 0.125. The base must be non-zero.

b^(1/n) is the n-th root of b. So 8^(1/3) = ∛8 = 2, and 16^(0.5) = √16 = 4. In general b^(p/q) = (b^p)^(1/q) — raise to the numerator, then take the denominator-th root.

The pattern b^3 → b^2 → b^1 continues by dividing by b each step, so b^0 = b^1 / b = 1. This holds for any non-zero base. The value of 0^0 is conventionally 1 in combinatorics and analysis, but mathematically indeterminate.

Also known as

exponent calculator
raise to power calculator
b to the n
base exponent result
negative exponent calculator
fractional exponent
exponentiation calculator

APA

TG we-Calculate Editorial Team. (2026). Math Power Calculator — Exponentiation (b^n) [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/math-power-calculator

Chicago

TG we-Calculate Editorial Team. "Math Power Calculator — Exponentiation (b^n)." TG we-Calculate. 2026. https://we-calculate.com/calculator/math-power-calculator.

IEEE

TG we-Calculate Editorial Team, "Math Power Calculator — Exponentiation (b^n)," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/math-power-calculator

BibTeX

@misc{wecalculate_math_power_calculator, title = {Math Power Calculator — Exponentiation (b^n)}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/math-power-calculator}}, year = {2026}, note = {TG we-Calculate} }

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