Exponent Calculator
Instantly calculate powers (xⁿ) for any base and exponent. Supports decimals, negatives, fractions, and scientific notation.
Base & Exponent
Result (xⁿ)
0
Instantly calculate powers (xⁿ) for any base and exponent. Supports decimals, negatives, fractions, and scientific notation.
The Exponent Calculator computes xⁿ — any base raised to any power. It handles whole numbers, negative exponents, decimal exponents, and fractional exponents (roots), making it useful for everything from basic arithmetic to scientific and financial calculations.
Result = xⁿ where x = base, n = exponent
Positive exponent: xⁿ = x × x × ... (n times) Zero exponent: x⁰ = 1 (any x ≠ 0) Negative exponent: x⁻ⁿ = 1 / xⁿ Fractional exponent: x^(1/n) = ⁿ√x (nth root of x) One as base: 1ⁿ = 1 (any n)
Fractional exponents are a compact way to express roots. Enter the decimal equivalent of the fraction:
x^(1/2) = x^0.5 = √x (square root) x^(1/3) = x^0.333 = ∛x (cube root) x^(m/n) = ⁿ√(xᵐ)
Seeing the full working makes the rules concrete. Here are three carried out in detail:
Example 1 — Whole-number power: 3⁴
3⁴ = 3 × 3 × 3 × 3
= 9 × 3 × 3
= 27 × 3
= 81
Example 2 — Negative exponent: 2⁻⁴
2⁻⁴ = 1 ÷ 2⁴
= 1 ÷ 16
= 0.0625
Example 3 — Fractional exponent (root): 16^0.25
16^0.25 = 16^(1/4) = ⁴√16
The 4th root of 16 is the number that, multiplied by
itself 4 times, equals 16. Since 2 × 2 × 2 × 2 = 16,
16^0.25 = 2 Exponents are the engine behind compound growth. Suppose you invest $1,000 at a 6% annual return for 20 years, compounded once per year:
A = P × (1 + r)ⁿ A = 1000 × (1 + 0.06)²⁰ A = 1000 × 1.06²⁰ A = 1000 × 3.207135... A ≈ $3,207.14
The money more than triples — and almost all of that growth comes from the exponent. To run your own numbers, use the Compound Interest Calculator.
Powers of 2 show up constantly in computing, doubling problems, and binary math:
| Exponent (n) | 2ⁿ | Common meaning |
|---|---|---|
| 2⁴ | 16 | Hex digit range |
| 2⁸ | 256 | One byte (0–255) |
| 2¹⁰ | 1,024 | 1 kilobyte (KB) |
| 2²⁰ | 1,048,576 | 1 megabyte (MB) |
| 2³⁰ | 1,073,741,824 | 1 gigabyte (GB) |
It computes xⁿ for any base and exponent — including whole numbers, decimals, negatives, and fractions. For example: 2⁵ = 32, 10⁻² = 0.01, 9^(0.5) = 3.
Any non-zero number raised to the power of 0 equals 1. For example, 5⁰ = 1, 100⁰ = 1, and (−7)⁰ = 1. The expression 0⁰ is mathematically indeterminate.
A negative exponent means take the reciprocal: x⁻ⁿ = 1 / xⁿ. For example, 10⁻² = 1 / 10² = 1/100 = 0.01, and 2⁻³ = 1/8 = 0.125. This is common in scientific notation and physics.
Yes. Fractional exponents represent roots: x^(1/2) = square root, x^(1/3) = cube root. For example, 9^(0.5) = 3 and 8^(0.333) ≈ 2. Enter the decimal equivalent of the fraction.
A negative base raised to an even exponent gives a positive result — e.g., (−2)⁴ = 16. An odd exponent gives a negative result — e.g., (−2)³ = −8. Fractional exponents with negative bases may produce complex (non-real) results.
Yes, decimal bases and exponents are fully supported. For very large results — beyond approximately 10³⁰⁸ — JavaScript's floating-point limit is reached and the result may display as Infinity.
Exponents appear in compound interest (A = P(1+r)ⁿ), scientific notation (3×10⁸ m/s), computer storage (2¹⁰ = 1 KB, 2²⁰ = 1 MB), population growth models, radiation decay, and algorithm complexity analysis.
In the expression 2⁵, the base is 2, the exponent is 5, and the whole expression (the result, 32) is the 'power.' In everyday use, 'exponent' and 'power' are often used interchangeably — '2 to the 5th power' means 2⁵. Strictly speaking, the exponent is the small raised number and the power is the value it produces.
x² is read 'x squared,' x³ is 'x cubed,' and x⁴ is 'x to the fourth power' (or just 'x to the fourth'). Squaring comes from the area of a square (side²) and cubing from the volume of a cube (side³), which is why those two have special names.
2¹⁰ = 1,024. This is a key number in computing because it is the number of values 10 binary bits can represent, and it is why a kilobyte is 1,024 bytes rather than exactly 1,000. Likewise 2²⁰ = 1,048,576 (a megabyte).
Order of operations applies the exponent before the negative sign, so −2⁴ means −(2⁴) = −16, while (−2)⁴ means (−2)×(−2)×(−2)×(−2) = 16. Always wrap a negative base in parentheses when you intend the whole negative number to be raised to the power.
1 raised to any exponent is always 1 (1⁵ = 1, 1⁻³ = 1). 0 raised to a positive exponent is 0 (0⁴ = 0), but 0 raised to a negative exponent is undefined because it requires dividing by zero, and 0⁰ is treated as indeterminate.
A logarithm is the inverse of an exponent: it answers 'what power do I raise the base to?' Since 2⁵ = 32, the base-2 logarithm of 32 is 5 (log₂32 = 5). Exponents build a number up by repeated multiplication; logarithms work backward to recover the exponent.