Exponent Calculator

Calculate x to the power of n for any base and exponent. Supports negative exponents, fractional exponents, and shows step-by-step working.

⚡ Quick Calculator Get a fast estimate

Base (x)

Can be any real number including negatives and fractions.

Exponent (n)

Can be negative (gives 1/xⁿ) or fractional (gives roots).

2^10

1024

Step-by-step

2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024

2^2

2^3

2^(-1)

0.5

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How to Use

Enter a base number (x) and an exponent (n) to calculate xⁿ. The exponent can be positive, negative, zero, or fractional.

The Extended Calculator adds a power growth chart, scientific notation conversion, a logarithm tab, and exponent rules reference. The Professional Calculator handles modular exponentiation, very large integer powers (via BigInt), and multi-base conversion.

Need more detail?

📊 Extended Calculator More options, charts, and scenario comparison

Base (b)

Exponent (n)

2^10

1024

Scientific Notation

1.024 × 10^3

Logarithm (base 10)

3.0103

Natural log

6.931472

Growth of 2^x

Exponent Rules

Basic: xⁿ = x × x × x ... (n times)

Zero exponent: x⁰ = 1 (for any x ≠ 0)

Negative exponent: x⁻ⁿ = 1 / xⁿ

Fractional exponent: x^(1/n) = ⁿ√x (nth root)

Product rule: xᵃ × xᵇ = x^(a+b)

Power rule: (xᵃ)ᵇ = x^(a×b)

Worked Examples

2^10: 2 × 2 × ... × 2 (10 times) = 1,024

3^(-2): 1 / 3² = 1 / 9 = 0.1111...

16^(0.5): √16 = 4

8^(1/3): ∛8 = 2

5^0: Any number to power 0 = 1

Need full precision?

🔬 Professional Calculator Complete parameters, sensitivity analysis, and detailed breakdown

(2)^(100) mod (1000000007) = ?

Base (b)

Exponent (e)

Modulus (m)

2^100 mod 1000000007

976371285

Algorithm

Fast Exponentiation (square-and-multiply)

Use cases: RSA encryption, Fermat's little theorem, primality testing, Diffie-Hellman key exchange.
Try: 2^100 mod 10 = 6 (last digit of 2^100)

Frequently Asked Questions

Because xⁿ / xⁿ = x^(n−n) = x⁰, and any non-zero number divided by itself equals 1. This definition keeps all exponent rules consistent (except 0⁰, which is technically undefined).

A negative exponent means take the reciprocal. x⁻ⁿ = 1/xⁿ. For example, 2⁻³ = 1/2³ = 1/8 = 0.125.

A fractional exponent represents a root. x^(1/n) is the nth root of x. More generally, x^(m/n) = (ⁿ√x)ᵐ. For example, 8^(2/3) = (∛8)² = 2² = 4.

Scientific notation expresses numbers as a × 10ⁿ where 1 ≤ a < 10. For example, 3,000,000 = 3 × 10⁶ and 0.00045 = 4.5 × 10⁻⁴. It uses powers of 10 to represent very large or small numbers compactly.

Compound interest uses A = P(1 + r)ⁿ where n is the number of compounding periods. This exponential formula explains why money grows faster over time with compound interest.

Exponent Calculator

How to Use

Exponent Rules

Worked Examples

Frequently Asked Questions

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