What is a negative exponent?

A negative exponent means the reciprocal: x⁻ⁿ = 1/xⁿ. Example: 2⁻³ = 1/2³ = 1/8 = 0.125. Negative exponents do NOT make the result negative — they indicate reciprocals.

What is a fractional exponent?

A fractional exponent represents a root: x^(1/n) = ⁿ√x and x^(m/n) = ⁿ√(xᵐ). Example: 8^(1/3) = ∛8 = 2, 4^(3/2) = (√4)³ = 2³ = 8.

What is anything to the power of 0?

Any non-zero number raised to the power 0 equals 1: x⁰ = 1 (for x≠0). This is because x⁰ = x^(n-n) = xⁿ/xⁿ = 1. The expression 0⁰ is mathematically indeterminate — it is typically taken as 1 in combinatorics but is undefined in analysis.

xⁿ Math Calculator

Exponent Calculator

Calculate any base raised to any power. Supports negative exponents, fractional exponents, zero exponent and scientific notation with step-by-step solutions.

Exponent type

Base (x)

Exponent (n)

e.g. 2^10 = 1024

Quick examples

2^8 —

—Exact value

—Scientific notation

—log₁₀(result)

Powers of 2

Exponent laws (with your base)

📝 Step-by-step solution

Exponent calculator guide

An exponent (or power) tells you how many times to multiply the base by itself. xⁿ = x × x × x … (n times). This calculator handles all types of exponents including negative, fractional, decimal and zero.

⁻ Negative exponents

x⁻ⁿ = 1/xⁿ. Example: 2⁻³ = 1/8 = 0.125. A negative exponent does NOT make the answer negative — it means you take the reciprocal. So 2⁻³ = 0.125, not −8.

½ Fractional exponents

x^(m/n) = ⁿ√(xᵐ). So x^(1/2) = √x, x^(1/3) = ∛x, x^(3/2) = (√x)³. Example: 27^(2/3) = (∛27)² = 3² = 9. You can compute the root first, then power — or power first, then root.

⁰ Zero exponent

x⁰ = 1 for any x≠0. This follows from the quotient rule: xⁿ/xⁿ = x^(n-n) = x⁰ = 1. The special case 0⁰ is indeterminate in general analysis but is often defined as 1 in combinatorics and limits.

🔢 Scientific notation

Large or small results are shown in scientific notation: a × 10ⁿ where 1 ≤ a < 10. Example: 2¹⁰ = 1024 = 1.024 × 10³. Useful for astronomy, physics and chemistry where numbers range from 10⁻³⁰ to 10⁸⁰.

Frequently asked questions

What are the laws of exponents?

Product rule: xᵃ × xᵇ = x^(a+b). Quotient rule: xᵃ / xᵇ = x^(a-b). Power rule: (xᵃ)ᵇ = x^(ab). Product of powers: (xy)ⁿ = xⁿyⁿ. Zero exponent: x⁰=1. Negative exponent: x⁻ⁿ=1/xⁿ. Fractional: x^(m/n)=ⁿ√(xᵐ). These rules make it possible to simplify complex expressions.

What is the difference between 2³ and 3²?

2³ = 2×2×2 = 8. 3² = 3×3 = 9. Exponentiation is NOT commutative — bᵃ ≠ aᵇ in general. The base is the number being multiplied, and the exponent tells how many times. 2³ means "2 multiplied 3 times" while 3² means "3 multiplied 2 times".

What is 0 raised to any power?

0ⁿ = 0 for any positive n. For example 0² = 0, 0¹⁰⁰ = 0. For negative exponents, 0⁻ⁿ is undefined (division by zero). The case 0⁰ is indeterminate (different values depending on the context and limit taken).