Exponents Calculator
Calculate a number raised to a power: enter the base and the exponent — negative, fractional, or scientific notation like 5e3 — and get the result with the step-by-step calculation, all computed in this browser tab.
Enter the base and the exponent, then press Calculate. The result and the step-by-step calculation appear here.
How it works: an multiplies the base by itself n times (2⁵ = 2×2×2×2×2 = 32); negative exponents use a⁻ⁿ = 1/aⁿ (2⁻³ = 0.125) and a⁰ = 1. The Calculation box evaluates expressions (and simplifies ones containing x). Exact decimal arithmetic, up to 8 significant digits; all math runs in this browser tab — nothing is uploaded, stored, or shared.
Enter the base
The number being multiplied: 2, -2, 2.5, or scientific notation such as 5e3 (= 5000) and 1.45e12. Negative bases work for any whole exponent.
Enter the exponent
How many times the base multiplies itself: positive (5), zero (a⁰ = 1), negative (2⁻³ = 1/8) or fractional (2⁰·⁵ = √2), and it may also use e notation.
Press Calculate
You get the result with up to 8 significant digits plus the calculation line: 2⁵ = 2×2×2×2×2 = 32, or 2⁻³ = 1/2³ = 1/(2×2×2) = 0.125. The expression box also evaluates inputs like 3^2*2.
Exponent calculation examples
| base | exponent | base^exponent | note |
|---|---|---|---|
| 2 | 5 | 32 | 2×2×2×2×2 |
| 2 | -3 | 0.125 | 1/2³ = 1/8 |
| -2 | 4 | 16 | (-2)×(-2)×(-2)×(-2) |
| 2.5 | 3 | 15.625 | 2.5×2.5×2.5 |
| 4 | 0 | 1 | zero exponent rule |
| 2 | 0.5 | 1.4142136 | √2, 8 significant digits |
| 4 | -0.5 | 0.5 | 1/4⁰·⁵ = 1/2 |
| 5e3 | 2 | 25000000 | e notation input |
| 2 | 100 | 1.2676506e30 | e notation output |
Exponent laws and rules
The exponent formula is aⁿ = a × a × … × a (n times): 2⁵ = 2×2×2×2×2 = 32. The laws that follow: multiplying aⁿ ⋅ aᵐ = aⁿ⁺ᵐ (2³ ⋅ 2⁴ = 2⁷ = 128), dividing aⁿ / aᵐ = aⁿ⁻ᵐ (2⁵ / 2³ = 2² = 4), power of an exponent (aⁿ)ᵐ = aⁿ·ᵐ ((2³)⁴ = 2¹² = 4096), negative exponent a⁻ⁿ = 1/aⁿ (2⁻³ = 1/8 = 0.125), and zero exponent a⁰ = 1 (4⁰ = 1).
How this calculator works
- What do the calculation steps show?
- For exponents between 2 and 30 in absolute value the product is written out: 2⁵ = 2×2×2×2×2 = 32. Negative exponents add the 1/aⁿ rule first: 2⁻³ = 1/2³ = 1/(2×2×2) = 0.125.
- How are big or tiny results shown?
- Results use exact decimal arithmetic with up to 8 significant digits. Large and small magnitudes switch to e notation — 2¹⁰⁰ = 1.2676506e30. Inputs in e notation (5e3, 4e-8) work too.
- Why does 2^31 show 2147483600 instead of 2147483648?
- Because the answer is capped at 8 significant digits like the reference tool: 2147483648 rounded to 8 significant digits is 2147483600. Exact values with 8 or fewer digits print exactly.
- When do I get "Syntax error!"?
- For malformed input, for 0 with a negative exponent (1/0 is undefined), and for negative bases with fractional exponents, whose result is not a real number (e.g. √-2). The calculator shows a clear error instead of a made-up number.
Privacy: this calculator runs entirely in your browser tab. Your input and results are never uploaded, stored, or shared.