Exponent Calculator

From squaring a number to computing scientific notation values, this exponent calculator handles any base raised to any power — including negative exponents and fractional (root) exponents.

How to Use This Calculator

1. Enter the base (the number being multiplied).
2. Enter the exponent (the power to raise the base to).
3. Click Calculate to see the result.

Exponent Rules

• xⁿ: Multiply x by itself n times. 2³ = 2 × 2 × 2 = 8
• x⁰ = 1: Any non-zero base to the 0 power equals 1.
• x⁻ⁿ = 1/xⁿ: Negative exponent → reciprocal. 2⁻³ = 1/8 = 0.125
• x^(1/n) = ⁿ√x: Fractional exponent → root. 8^(1/3) = ∛8 = 2
• xᵃ × xᵇ = x^(a+b): Multiply same base → add exponents
• (xᵃ)ᵇ = x^(ab): Power of a power → multiply exponents

Example Calculations

• 5⁴ = 5 × 5 × 5 × 5 = 625
• 10⁻³ = 1/1000 = 0.001
• 16^(0.5) = √16 = 4
• 2^10 = 1,024
• e^1 ≈ 2.71828 (Euler's number)

Real-World Applications

• Compound interest: A = P(1+r)ⁿ — the n exponent drives growth.
• Scientific notation: 6.022 × 10²³ (Avogadro's number) uses exponents.
• Computer memory: 1 GB = 2³⁰ bytes = 1,073,741,824 bytes.
• Decibels: Sound intensity scales are logarithmic/exponential.

Common Mistakes to Avoid

• Confusing -x² and (-x)²: −3² = −9, but (−3)² = 9. The exponent applies only to the base, not the negative sign, unless parentheses indicate otherwise.
• Misapplying exponent rules to sums: (a+b)² ≠ a² + b². This is a very common algebra error — always expand using FOIL or distribution.
• Confusing 2³ and 2×3: 2³ = 8, while 2×3 = 6. Exponentiation and multiplication are very different operations.

Frequently Asked Questions

What is 0⁰?

Mathematically undefined or 1 depending on context. In combinatorics and many formulas it's treated as 1. In limits, 0⁰ is an indeterminate form.

What is the difference between power and exponent?

They're often used interchangeably. In xⁿ, x is the base, n is the exponent, and xⁿ is the "power." Saying "2 to the power of 3" and "2 with exponent 3" both mean 2³ = 8.

How are exponents used in scientific notation?

Scientific notation writes numbers as a × 10ⁿ. 93,000,000 miles = 9.3 × 10⁷. This makes very large or small numbers easier to read and work with. See our Scientific Notation Calculator.

Conclusion

Exponents are the language of growth, decay, and scale. From basic algebra to compound interest to computer science, this calculator handles every exponentiation problem — large or small, positive or negative.

Related: Root Calculator | Log Calculator | Scientific Notation Calculator | Compound Interest Calculator