Exponent Calculator

Instantly calculate powers (xⁿ) for any base and exponent. Supports decimals, negatives, fractions, and scientific notation.

Base & Exponent
Result (xⁿ)
0

About the Exponent Calculator

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.

Formula

Result = xⁿ   where x = base, n = exponent

Key Exponent Rules

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)

Examples

  • 2⁵ = 2 × 2 × 2 × 2 × 2 = 32
  • 10³ = 1,000
  • 5⁰ = 1
  • 10⁻² = 1 ÷ 100 = 0.01
  • 9^(0.5) = √9 = 3 (square root)
  • 8^(0.333) ≈ ∛8 = 2 (cube root)
  • (−2)⁴ = 16 (negative base, even exponent → positive)
  • (−2)³ = −8 (negative base, odd exponent → negative)

Negative Base Rules

  • Negative base + even exponent → positive result (e.g., (−3)² = 9)
  • Negative base + odd exponent → negative result (e.g., (−3)³ = −27)
  • Negative base + fractional exponent → may produce non-real results

Fractional Exponents and Roots

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)

Real-World Applications

  • Compound interest: A = P(1 + r)ⁿ — how investments grow over time. Try our Compound Interest Calculator.
  • Scientific notation: 3.0 × 10⁸ m/s (speed of light)
  • Computer storage: 2¹⁰ = 1,024 bytes (1 KB), 2²⁰ = 1 MB, 2³⁰ = 1 GB
  • Population growth: exponential growth models using eʳᵗ
  • Physics: inverse-square law — intensity ∝ 1/r²
  • Algorithms: time complexity such as O(n²) or O(2ⁿ)

Frequently Asked Questions

What does the Exponent Calculator do?

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.

What is any number to the power of 0?

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.

How do negative exponents work?

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.

Can it compute fractional exponents like 9^(1/2)?

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.

How do negative bases behave with different exponents?

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.

Does it support decimals or very large numbers?

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.

Where are exponents used in real life?

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.